.5(x+4)(2x+14)=108

Solution for .5(x+4)(2x+14)=108 equation:

Simplifying
0.5(x + 4)(2x + 14) = 108

Reorder the terms:
0.5(4 + x)(2x + 14) = 108

Reorder the terms:
0.5(4 + x)(14 + 2x) = 108

Multiply (4 + x) * (14 + 2x)
0.5(4(14 + 2x) + x(14 + 2x)) = 108
0.5((14 * 4 + 2x * 4) + x(14 + 2x)) = 108
0.5((56 + 8x) + x(14 + 2x)) = 108
0.5(56 + 8x + (14 * x + 2x * x)) = 108
0.5(56 + 8x + (14x + 2x2)) = 108

Combine like terms: 8x + 14x = 22x
0.5(56 + 22x + 2x2) = 108
(56 * 0.5 + 22x * 0.5 + 2x2 * 0.5) = 108
(28 + 11x + 1x2) = 108

Solving
28 + 11x + 1x2 = 108

Solving for variable 'x'.

Reorder the terms:
28 + -108 + 11x + 1x2 = 108 + -108

Combine like terms: 28 + -108 = -80
-80 + 11x + 1x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-80 + 11x + 1x2 = 0

Factor a trinomial.
(-16 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-16, 5}