(x-6)(x-6)(3)=432

Solution for (x-6)(x-6)(3)=432 equation:

Simplifying
(x + -6)(x + -6)(3) = 432

Reorder the terms:
(-6 + x)(x + -6)(3) = 432

Reorder the terms:
(-6 + x)(-6 + x)(3) = 432

Reorder the terms for easier multiplication:
3(-6 + x)(-6 + x) = 432

Multiply (-6 + x) * (-6 + x)
3(-6(-6 + x) + x(-6 + x)) = 432
3((-6 * -6 + x * -6) + x(-6 + x)) = 432
3((36 + -6x) + x(-6 + x)) = 432
3(36 + -6x + (-6 * x + x * x)) = 432
3(36 + -6x + (-6x + x2)) = 432

Combine like terms: -6x + -6x = -12x
3(36 + -12x + x2) = 432
(36 * 3 + -12x * 3 + x2 * 3) = 432
(108 + -36x + 3x2) = 432

Solving
108 + -36x + 3x2 = 432

Solving for variable 'x'.

Reorder the terms:
108 + -432 + -36x + 3x2 = 432 + -432

Combine like terms: 108 + -432 = -324
-324 + -36x + 3x2 = 432 + -432

Combine like terms: 432 + -432 = 0
-324 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-108 + -12x + x2) = 0

Factor a trinomial.
3((-6 + -1x)(18 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {-6, 18}