How do you use factoring to solve this equation #x^2-12x+27=0#?

Question

Nathan Axel · Accepted Answer

#x^2 -12x+27=0# We can Split the Middle Term of this expression to factorise it and thereby find the solution.
In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that: #N_1*N_2 = a*c = 1*27 = 27#
And
N_1 +N_2 = b = -12# After trying out a few numbers we get #N_1 = -9# and #N_2 =-3#
#9*3 = 27# and #-9+(-3)= -12#  #x^2 -12x+27= x^2 -9x - 3x +27#
#x(x - 9) - 3(x-9) = 0# #color(green)((x-9)(x - 3)# is the factorised form.
and #color(green)(x=9 and x=3# are the solutions.

Abigail Allen · Answer

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NextTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

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Next,To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

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Next, factorTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

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Next, factor byTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

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Next, factor by grouping:

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$x^2 - 12x + 27 =To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

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$x^2 - 12x + 27 = xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

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Next, factor by grouping:

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$x^2 - 12x + 27 = x^2 - 3x - 9x + To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

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$x^2 - 12x + 27 = x^2 - 3x - 9x + 27To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

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$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

To solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

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$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

NextTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3)To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next,To solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) -To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factorTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor byTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(xTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by groupingTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x -To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

To solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3)To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) =To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0\To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

NowTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now,To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, noticeTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice thatTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x +To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that \To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 =To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)\To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ isTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a commonTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3)To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factorTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

\To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(xTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x -To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)\To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x -To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

NowTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a commonTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factorTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9)To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor,To solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product propertyTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, soTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$xTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{orTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or}To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quadTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad xTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0\To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

STo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zeroTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

SolveTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero givesTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve forTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives youTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you theTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutionsTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x\To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

To solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$xTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x =To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quadTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \RightarrowTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{orTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or}To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x =To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quadTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad xTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3\To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x =To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

To solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9\To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x -To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

\[x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ andTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 =To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ and $To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 = 0To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ and $xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 = 0 \Rightarrow x = 9$

Therefore, the solutions toTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ and $x =To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 = 0 \Rightarrow x = 9$

Therefore, the solutions to theTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ and $x = To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 = 0 \Rightarrow x = 9$

Therefore, the solutions to the equationTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ and $x = 9To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 = 0 \Rightarrow x = 9$

Therefore, the solutions to the equation areTo solve the equation $x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ and $x = 9\To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 = 0 \Rightarrow x = 9$

Therefore, the solutions to the equation are $To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ and $x = 9$.To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 = 0 \Rightarrow x = 9$

Therefore, the solutions to the equation are $xTo solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ and $x = 9$.To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 = 0 \Rightarrow x = 9$

Therefore, the solutions to the equation are $x =To solve the equation \(x^2 - 12x + 27 = 0$ using factoring, first, identify two numbers that multiply to give $27$ and add to give $-12$. These numbers are $-3$ and $-9$. Then, rewrite the middle term $ -12x$ using these numbers:

$$x^2 - 3x - 9x + 27 = 0$$

Next, factor by grouping:

$$x(x - 3) - 9(x - 3) = 0$$

Now, notice that $(x - 3)$ is a common factor:

$$(x - 3)(x - 9) = 0$$

Apply the zero-product property:

$$x - 3 = 0 \quad \text{or} \quad x - 9 = 0$$

Solve for $x$:

$$x = 3 \quad \text{or} \quad x = 9$$

So, the solutions to the equation are $x = 3$ and $x = 9$.To solve the equation $x^2 - 12x + 27 = 0$ using factoring, you first look for two numbers that multiply to $27$ and add up to $-12$. These numbers are $-3$ and $-9$. Then, you rewrite the middle term $ -12x $ as the sum of these two numbers:

$x^2 - 12x + 27 = x^2 - 3x - 9x + 27$

Next, factor by grouping:

$x^2 - 3x - 9x + 27 = x(x - 3) - 9(x - 3)$

Now, notice that $x - 3$ is a common factor, so you can factor it out:

$x(x - 3) - 9(x - 3) = (x - 3)(x - 9)$

Setting each factor equal to zero gives you the solutions:

$x - 3 = 0 \Rightarrow x = 3$

$x - 9 = 0 \Rightarrow x = 9$

Therefore, the solutions to the equation are $x = 3$ and $x = 9$.