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

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

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

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

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

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

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

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

Solving
21 + 10x + 1x2 = 117

Solving for variable 'x'.

Reorder the terms:
21 + -117 + 10x + 1x2 = 117 + -117

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

Combine like terms: 117 + -117 = 0
-96 + 10x + 1x2 = 0

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

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 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 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
Subproblem 2
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
Solution
x = {-16, 6}