110=.5(x+4)(2x+6)

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Solution for 110=.5(x+4)(2x+6) equation: 


Simplifying
110 = 0.5(x + 4)(2x + 6)

Reorder the terms:
110 = 0.5(4 + x)(2x + 6)

Reorder the terms:
110 = 0.5(4 + x)(6 + 2x)

Multiply (4 + x) * (6 + 2x)
110 = 0.5(4(6 + 2x) + x(6 + 2x))
110 = 0.5((6 * 4 + 2x * 4) + x(6 + 2x))
110 = 0.5((24 + 8x) + x(6 + 2x))
110 = 0.5(24 + 8x + (6 * x + 2x * x))
110 = 0.5(24 + 8x + (6x + 2x2))

Combine like terms: 8x + 6x = 14x
110 = 0.5(24 + 14x + 2x2)
110 = (24 * 0.5 + 14x * 0.5 + 2x2 * 0.5)
110 = (12 + 7x + 1x2)

Solving
110 = 12 + 7x + 1x2

Solving for variable 'x'.

Combine like terms: 110 + -12 = 98
98 + -7x + -1x2 = 12 + 7x + 1x2 + -12 + -7x + -1x2

Reorder the terms:
98 + -7x + -1x2 = 12 + -12 + 7x + -7x + 1x2 + -1x2

Combine like terms: 12 + -12 = 0
98 + -7x + -1x2 = 0 + 7x + -7x + 1x2 + -1x2
98 + -7x + -1x2 = 7x + -7x + 1x2 + -1x2

Combine like terms: 7x + -7x = 0
98 + -7x + -1x2 = 0 + 1x2 + -1x2
98 + -7x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
98 + -7x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(14 + 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 '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
Solution
x = {7, -14}

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