110=.5(x+5)(2x+12)

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Solution for 110=.5(x+5)(2x+12) equation: 


Simplifying
110 = 0.5(x + 5)(2x + 12)

Reorder the terms:
110 = 0.5(5 + x)(2x + 12)

Reorder the terms:
110 = 0.5(5 + x)(12 + 2x)

Multiply (5 + x) * (12 + 2x)
110 = 0.5(5(12 + 2x) + x(12 + 2x))
110 = 0.5((12 * 5 + 2x * 5) + x(12 + 2x))
110 = 0.5((60 + 10x) + x(12 + 2x))
110 = 0.5(60 + 10x + (12 * x + 2x * x))
110 = 0.5(60 + 10x + (12x + 2x2))

Combine like terms: 10x + 12x = 22x
110 = 0.5(60 + 22x + 2x2)
110 = (60 * 0.5 + 22x * 0.5 + 2x2 * 0.5)
110 = (30 + 11x + 1x2)

Solving
110 = 30 + 11x + 1x2

Solving for variable 'x'.

Combine like terms: 110 + -30 = 80
80 + -11x + -1x2 = 30 + 11x + 1x2 + -30 + -11x + -1x2

Reorder the terms:
80 + -11x + -1x2 = 30 + -30 + 11x + -11x + 1x2 + -1x2

Combine like terms: 30 + -30 = 0
80 + -11x + -1x2 = 0 + 11x + -11x + 1x2 + -1x2
80 + -11x + -1x2 = 11x + -11x + 1x2 + -1x2

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

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

Factor a trinomial.
(5 + -1x)(16 + x) = 0


Subproblem 1
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

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 = {5, -16}

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