108=(x-6)(x-6)3

Solution for 108=(x-6)(x-6)3 equation:

Simplifying
108 = (x + -6)(x + -6) * 3

Reorder the terms:
108 = (-6 + x)(x + -6) * 3

Reorder the terms:
108 = (-6 + x)(-6 + x) * 3

Reorder the terms for easier multiplication:
108 = 3(-6 + x)(-6 + x)

Multiply (-6 + x) * (-6 + x)
108 = 3(-6(-6 + x) + x(-6 + x))
108 = 3((-6 * -6 + x * -6) + x(-6 + x))
108 = 3((36 + -6x) + x(-6 + x))
108 = 3(36 + -6x + (-6 * x + x * x))
108 = 3(36 + -6x + (-6x + x2))

Combine like terms: -6x + -6x = -12x
108 = 3(36 + -12x + x2)
108 = (36 * 3 + -12x * 3 + x2 * 3)
108 = (108 + -36x + 3x2)

Add '-108' to each side of the equation.
108 + -108 = 108 + -36x + -108 + 3x2

Combine like terms: 108 + -108 = 0
0 = 108 + -36x + -108 + 3x2

Reorder the terms:
0 = 108 + -108 + -36x + 3x2

Combine like terms: 108 + -108 = 0
0 = 0 + -36x + 3x2
0 = -36x + 3x2

Solving
0 = -36x + 3x2

Solving for variable 'x'.
Remove the zero:
36x + -3x2 = -36x + 3x2 + 36x + -3x2

Reorder the terms:
36x + -3x2 = -36x + 36x + 3x2 + -3x2

Combine like terms: -36x + 36x = 0
36x + -3x2 = 0 + 3x2 + -3x2
36x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
36x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(12 + -1x) = 0

Ignore the factor 3.
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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {0, 12}