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

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

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

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

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

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

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

Solving
117 = 12 + 8x + x2

Solving for variable 'x'.

Combine like terms: 117 + -12 = 105
105 + -8x + -1x2 = 12 + 8x + x2 + -12 + -8x + -1x2

Reorder the terms:
105 + -8x + -1x2 = 12 + -12 + 8x + -8x + x2 + -1x2

Combine like terms: 12 + -12 = 0
105 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2
105 + -8x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
105 + -8x + -1x2 = 0 + x2 + -1x2
105 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
105 + -8x + -1x2 = 0

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

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

Simplifying
15 + x = 0

Solving
15 + x = 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 + x = 0 + -15

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

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

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