(12v+4)(8v-12)=0

Solution for (12v+4)(8v-12)=0 equation:

Simplifying
(12v + 4)(8v + -12) = 0

Reorder the terms:
(4 + 12v)(8v + -12) = 0

Reorder the terms:
(4 + 12v)(-12 + 8v) = 0

Multiply (4 + 12v) * (-12 + 8v)
(4(-12 + 8v) + 12v * (-12 + 8v)) = 0
((-12 * 4 + 8v * 4) + 12v * (-12 + 8v)) = 0
((-48 + 32v) + 12v * (-12 + 8v)) = 0
(-48 + 32v + (-12 * 12v + 8v * 12v)) = 0
(-48 + 32v + (-144v + 96v2)) = 0

Combine like terms: 32v + -144v = -112v
(-48 + -112v + 96v2) = 0

Solving
-48 + -112v + 96v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-3 + -7v + 6v2) = 0

Factor a trinomial.
16((-1 + -3v)(3 + -2v)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-1 + -3v)' equal to zero and attempt to solve:

Simplifying
-1 + -3v = 0

Solving
-1 + -3v = 0

Move all terms containing v to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -3v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3v = 0 + 1
-3v = 0 + 1

Combine like terms: 0 + 1 = 1
-3v = 1

Divide each side by '-3'.
v = -0.3333333333

Simplifying
v = -0.3333333333
Subproblem 2
Set the factor '(3 + -2v)' equal to zero and attempt to solve:

Simplifying
3 + -2v = 0

Solving
3 + -2v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2v = 0 + -3
-2v = 0 + -3

Combine like terms: 0 + -3 = -3
-2v = -3

Divide each side by '-2'.
v = 1.5

Simplifying
v = 1.5
Solution
v = {-0.3333333333, 1.5}