3(x-4)(2x-4)=0

Solution for 3(x-4)(2x-4)=0 equation:

Simplifying
3(x + -4)(2x + -4) = 0

Reorder the terms:
3(-4 + x)(2x + -4) = 0

Reorder the terms:
3(-4 + x)(-4 + 2x) = 0

Multiply (-4 + x) * (-4 + 2x)
3(-4(-4 + 2x) + x(-4 + 2x)) = 0
3((-4 * -4 + 2x * -4) + x(-4 + 2x)) = 0
3((16 + -8x) + x(-4 + 2x)) = 0
3(16 + -8x + (-4 * x + 2x * x)) = 0
3(16 + -8x + (-4x + 2x2)) = 0

Combine like terms: -8x + -4x = -12x
3(16 + -12x + 2x2) = 0
(16 * 3 + -12x * 3 + 2x2 * 3) = 0
(48 + -36x + 6x2) = 0

Solving
48 + -36x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + -6x + x2) = 0

Factor a trinomial.
6((2 + -1x)(4 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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
Solution
x = {2, 4}