(4x-12)(4x+6)=0

Solution for (4x-12)(4x+6)=0 equation:

Simplifying
(4x + -12)(4x + 6) = 0

Reorder the terms:
(-12 + 4x)(4x + 6) = 0

Reorder the terms:
(-12 + 4x)(6 + 4x) = 0

Multiply (-12 + 4x) * (6 + 4x)
(-12(6 + 4x) + 4x * (6 + 4x)) = 0
((6 * -12 + 4x * -12) + 4x * (6 + 4x)) = 0
((-72 + -48x) + 4x * (6 + 4x)) = 0
(-72 + -48x + (6 * 4x + 4x * 4x)) = 0
(-72 + -48x + (24x + 16x2)) = 0

Combine like terms: -48x + 24x = -24x
(-72 + -24x + 16x2) = 0

Solving
-72 + -24x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-9 + -3x + 2x2) = 0

Factor a trinomial.
8((-3 + -2x)(3 + -1x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

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

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

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

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

Simplifying
x = -1.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.5, 3}