117=(.5)(2x+14)(x+3)

Solution for 117=(.5)(2x+14)(x+3) equation:

Simplifying
117 = (0.5)(2x + 14)(x + 3)

Reorder the terms:
117 = 0.5(14 + 2x)(x + 3)

Reorder the terms:
117 = 0.5(14 + 2x)(3 + x)

Multiply (14 + 2x) * (3 + x)
117 = 0.5(14(3 + x) + 2x * (3 + x))
117 = 0.5((3 * 14 + x * 14) + 2x * (3 + x))
117 = 0.5((42 + 14x) + 2x * (3 + x))
117 = 0.5(42 + 14x + (3 * 2x + x * 2x))
117 = 0.5(42 + 14x + (6x + 2x2))

Combine like terms: 14x + 6x = 20x
117 = 0.5(42 + 20x + 2x2)
117 = (42 * 0.5 + 20x * 0.5 + 2x2 * 0.5)
117 = (21 + 10x + 1x2)

Solving
117 = 21 + 10x + 1x2

Solving for variable 'x'.

Combine like terms: 117 + -21 = 96
96 + -10x + -1x2 = 21 + 10x + 1x2 + -21 + -10x + -1x2

Reorder the terms:
96 + -10x + -1x2 = 21 + -21 + 10x + -10x + 1x2 + -1x2

Combine like terms: 21 + -21 = 0
96 + -10x + -1x2 = 0 + 10x + -10x + 1x2 + -1x2
96 + -10x + -1x2 = 10x + -10x + 1x2 + -1x2

Combine like terms: 10x + -10x = 0
96 + -10x + -1x2 = 0 + 1x2 + -1x2
96 + -10x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
96 + -10x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(16 + x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {6, -16}