(8-2x)(12-2x)x=0

Solution for (8-2x)(12-2x)x=0 equation:

Simplifying
(8 + -2x)(12 + -2x) * x = 0

Reorder the terms for easier multiplication:
x(8 + -2x)(12 + -2x) = 0

Multiply (8 + -2x) * (12 + -2x)
x(8(12 + -2x) + -2x * (12 + -2x)) = 0
x((12 * 8 + -2x * 8) + -2x * (12 + -2x)) = 0
x((96 + -16x) + -2x * (12 + -2x)) = 0
x(96 + -16x + (12 * -2x + -2x * -2x)) = 0
x(96 + -16x + (-24x + 4x2)) = 0

Combine like terms: -16x + -24x = -40x
x(96 + -40x + 4x2) = 0
(96 * x + -40x * x + 4x2 * x) = 0
(96x + -40x2 + 4x3) = 0

Solving
96x + -40x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(24 + -10x + x2) = 0

Factor a trinomial.
4x((4 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 4, 6}