(x-4)(x+8)=108

Solution for (x-4)(x+8)=108 equation:

Simplifying
(x + -4)(x + 8) = 108

Reorder the terms:
(-4 + x)(x + 8) = 108

Reorder the terms:
(-4 + x)(8 + x) = 108

Multiply (-4 + x) * (8 + x)
(-4(8 + x) + x(8 + x)) = 108
((8 * -4 + x * -4) + x(8 + x)) = 108
((-32 + -4x) + x(8 + x)) = 108
(-32 + -4x + (8 * x + x * x)) = 108
(-32 + -4x + (8x + x2)) = 108

Combine like terms: -4x + 8x = 4x
(-32 + 4x + x2) = 108

Solving
-32 + 4x + x2 = 108

Solving for variable 'x'.

Reorder the terms:
-32 + -108 + 4x + x2 = 108 + -108

Combine like terms: -32 + -108 = -140
-140 + 4x + x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-140 + 4x + x2 = 0

Factor a trinomial.
(-14 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
Subproblem 2
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
Solution
x = {-14, 10}