(x+6)(x)(6)=432

Solution for (x+6)(x)(6)=432 equation:

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

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

Reorder the terms for easier multiplication:
6x(6 + x) = 432
(6 * 6x + x * 6x) = 432
(36x + 6x2) = 432

Solving
36x + 6x2 = 432

Solving for variable 'x'.

Reorder the terms:
-432 + 36x + 6x2 = 432 + -432

Combine like terms: 432 + -432 = 0
-432 + 36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-72 + 6x + x2) = 0

Factor a trinomial.
6((-12 + -1x)(6 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
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 = {-12, 6}