How do you solve #4(3n - 2) (4n + 1) = 0#?

Question

Isaiah Anthony · Accepted Answer

#n=2/3 and -1/4#

According to one interpretation of the equation, either or both of the three factors have to be zero in order for the statement to be true. The product of multiplying the three factors, 4, (3n-2), and (4n+1), is 0.

you can see it this way #(4)\cdot(0)\cdot(4n+1)=0# or #(4)\cdot(3n-2)\cdot(0)=0# or #(4)\cdot(0)\cdot(0)=0#

Which means to say, that the factor #(3n-2)# and/or #(4n+1)# should be zero.

So, #3n-2=0# #=>3n=2# #=>n=2/3#

Also, #4n+1=0# #=>4n=-1# #=>n=-1/4#

Therefore, #n=2/3 and -1/4#

An alternative approach is to multiply the entire expression and divide it longwise; the result should be the same.

Eva Adamson · Answer

undefined To solve the equation 4(3n - 2)(4n + 1) = 0, you set each factor equal to zero and solve for n.

1. Setting 4 equal to zero: No solution.
2. Setting (3n - 2) equal to zero: 
   3n - 2 = 0
   3n = 2
   n = 2/3

3. Setting (4n + 1) equal to zero:
   4n + 1 = 0
   4n = -1
   n = -1/4

So the solutions are n = 2/3 and n = -1/4.