3(x+6)3(x+6)=36

Solution for 3(x+6)3(x+6)=36 equation:

Simplifying
3(x + 6) * 3(x + 6) = 36

Reorder the terms:
3(6 + x) * 3(x + 6) = 36

Reorder the terms:
3(6 + x) * 3(6 + x) = 36

Reorder the terms for easier multiplication:
3 * 3(6 + x)(6 + x) = 36

Multiply 3 * 3
9(6 + x)(6 + x) = 36

Multiply (6 + x) * (6 + x)
9(6(6 + x) + x(6 + x)) = 36
9((6 * 6 + x * 6) + x(6 + x)) = 36
9((36 + 6x) + x(6 + x)) = 36
9(36 + 6x + (6 * x + x * x)) = 36
9(36 + 6x + (6x + x2)) = 36

Combine like terms: 6x + 6x = 12x
9(36 + 12x + x2) = 36
(36 * 9 + 12x * 9 + x2 * 9) = 36
(324 + 108x + 9x2) = 36

Solving
324 + 108x + 9x2 = 36

Solving for variable 'x'.

Reorder the terms:
324 + -36 + 108x + 9x2 = 36 + -36

Combine like terms: 324 + -36 = 288
288 + 108x + 9x2 = 36 + -36

Combine like terms: 36 + -36 = 0
288 + 108x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(32 + 12x + x2) = 0

Factor a trinomial.
9((8 + x)(4 + x)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {-8, -4}