(x+4)(2x+2)-108=0

Solution for (x+4)(2x+2)-108=0 equation:

Simplifying
(x + 4)(2x + 2) + -108 = 0

Reorder the terms:
(4 + x)(2x + 2) + -108 = 0

Reorder the terms:
(4 + x)(2 + 2x) + -108 = 0

Multiply (4 + x) * (2 + 2x)
(4(2 + 2x) + x(2 + 2x)) + -108 = 0
((2 * 4 + 2x * 4) + x(2 + 2x)) + -108 = 0
((8 + 8x) + x(2 + 2x)) + -108 = 0
(8 + 8x + (2 * x + 2x * x)) + -108 = 0
(8 + 8x + (2x + 2x2)) + -108 = 0

Combine like terms: 8x + 2x = 10x
(8 + 10x + 2x2) + -108 = 0

Reorder the terms:
8 + -108 + 10x + 2x2 = 0

Combine like terms: 8 + -108 = -100
-100 + 10x + 2x2 = 0

Solving
-100 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 5x + x2) = 0

Factor a trinomial.
2((-10 + -1x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-10, 5}