How do you solve #6x^2+ 7x - 20 = 0# by factoring?

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To solve the quadratic equation (6x^2 + 7x - 20 = 0) by factoring, follow these steps:

1. Multiply the coefficient of (x^2) (which is 6) by the constant term (which is -20). You get -120.

2. Find two numbers that multiply to -120 and add up to the coefficient of (x) (which is 7). These numbers are 15 and -8.

3. Rewrite the middle term (7x) using these numbers: [6x^2 + 15x - 8x - 20 = 0]

4. Group the terms and factor by grouping: [(6x^2 + 15x) + (-8x - 20) = 0] [3x(2x + 5) - 4(2x + 5) = 0]

5. Notice that ((2x + 5)) is a common factor: [(3x - 4)(2x + 5) = 0]

6. Now, set each factor equal to zero and solve for (x): [3x - 4 = 0 \quad \text{or} \quad 2x + 5 = 0]

7. Solve each equation: [3x = 4 \quad \text{or} \quad 2x = -5] [x = \frac{4}{3} \quad \text{or} \quad x = -\frac{5}{2}]

So, the solutions to the equation (6x^2 + 7x - 20 = 0) by factoring are (x = \frac{4}{3}) and (x = -\frac{5}{2}).