(x+2)(x+6)=117

Solution for (x+2)(x+6)=117 equation:

Simplifying
(x + 2)(x + 6) = 117

Reorder the terms:
(2 + x)(x + 6) = 117

Reorder the terms:
(2 + x)(6 + x) = 117

Multiply (2 + x) * (6 + x)
(2(6 + x) + x(6 + x)) = 117
((6 * 2 + x * 2) + x(6 + x)) = 117
((12 + 2x) + x(6 + x)) = 117
(12 + 2x + (6 * x + x * x)) = 117
(12 + 2x + (6x + x2)) = 117

Combine like terms: 2x + 6x = 8x
(12 + 8x + x2) = 117

Solving
12 + 8x + x2 = 117

Solving for variable 'x'.

Reorder the terms:
12 + -117 + 8x + x2 = 117 + -117

Combine like terms: 12 + -117 = -105
-105 + 8x + x2 = 117 + -117

Combine like terms: 117 + -117 = 0
-105 + 8x + x2 = 0

Factor a trinomial.
(-15 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-15, 7}