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

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

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

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

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

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

Combine like terms: 10x + 12x = 22x
110 = (60 + 22x + 2x2)

Solving
110 = 60 + 22x + 2x2

Solving for variable 'x'.

Combine like terms: 110 + -60 = 50
50 + -22x + -2x2 = 60 + 22x + 2x2 + -60 + -22x + -2x2

Reorder the terms:
50 + -22x + -2x2 = 60 + -60 + 22x + -22x + 2x2 + -2x2

Combine like terms: 60 + -60 = 0
50 + -22x + -2x2 = 0 + 22x + -22x + 2x2 + -2x2
50 + -22x + -2x2 = 22x + -22x + 2x2 + -2x2

Combine like terms: 22x + -22x = 0
50 + -22x + -2x2 = 0 + 2x2 + -2x2
50 + -22x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
50 + -22x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -11x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(25 + -11x + -1x2)' equal to zero and attempt to solve:

Simplifying
25 + -11x + -1x2 = 0

Solving
25 + -11x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-25 + 11x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 11x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 11x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 11x + x2 = 0 + 25
11x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
11x + x2 = 25

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 25 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 25 + 30.25

Combine like terms: 25 + 30.25 = 55.25
30.25 + 11x + x2 = 55.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 55.25

Calculate the square root of the right side: 7.433034374

Break this problem into two subproblems by setting 
(x + 5.5) equal to 7.433034374 and -7.433034374.

Subproblem 1
x + 5.5 = 7.433034374

Simplifying
x + 5.5 = 7.433034374

Reorder the terms:
5.5 + x = 7.433034374

Solving
5.5 + x = 7.433034374

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 7.433034374 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 7.433034374 + -5.5
x = 7.433034374 + -5.5

Combine like terms: 7.433034374 + -5.5 = 1.933034374
x = 1.933034374

Simplifying
x = 1.933034374

Subproblem 2
x + 5.5 = -7.433034374

Simplifying
x + 5.5 = -7.433034374

Reorder the terms:
5.5 + x = -7.433034374

Solving
5.5 + x = -7.433034374

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -7.433034374 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -7.433034374 + -5.5
x = -7.433034374 + -5.5

Combine like terms: -7.433034374 + -5.5 = -12.933034374
x = -12.933034374

Simplifying
x = -12.933034374

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.933034374, -12.933034374}
Solution
x = {1.933034374, -12.933034374}