(x+2)(2x+2)=110

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

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

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

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

Multiply (2 + x) * (2 + 2x)
(2(2 + 2x) + x(2 + 2x)) = 110
((2 * 2 + 2x * 2) + x(2 + 2x)) = 110
((4 + 4x) + x(2 + 2x)) = 110
(4 + 4x + (2 * x + 2x * x)) = 110
(4 + 4x + (2x + 2x2)) = 110

Combine like terms: 4x + 2x = 6x
(4 + 6x + 2x2) = 110

Solving
4 + 6x + 2x2 = 110

Solving for variable 'x'.

Reorder the terms:
4 + -110 + 6x + 2x2 = 110 + -110

Combine like terms: 4 + -110 = -106
-106 + 6x + 2x2 = 110 + -110

Combine like terms: 110 + -110 = 0
-106 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-53 + 3x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-53 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-53 + 3x + x2 = 0

Solving
-53 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '53' to each side of the equation.
-53 + 3x + 53 + x2 = 0 + 53

Reorder the terms:
-53 + 53 + 3x + x2 = 0 + 53

Combine like terms: -53 + 53 = 0
0 + 3x + x2 = 0 + 53
3x + x2 = 0 + 53

Combine like terms: 0 + 53 = 53
3x + x2 = 53

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 53 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 53 + 2.25

Combine like terms: 53 + 2.25 = 55.25
2.25 + 3x + x2 = 55.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 55.25

Calculate the square root of the right side: 7.433034374

Break this problem into two subproblems by setting 
(x + 1.5) equal to 7.433034374 and -7.433034374.

Subproblem 1
x + 1.5 = 7.433034374

Simplifying
x + 1.5 = 7.433034374

Reorder the terms:
1.5 + x = 7.433034374

Solving
1.5 + x = 7.433034374

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 7.433034374 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 7.433034374 + -1.5
x = 7.433034374 + -1.5

Combine like terms: 7.433034374 + -1.5 = 5.933034374
x = 5.933034374

Simplifying
x = 5.933034374

Subproblem 2
x + 1.5 = -7.433034374

Simplifying
x + 1.5 = -7.433034374

Reorder the terms:
1.5 + x = -7.433034374

Solving
1.5 + x = -7.433034374

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -7.433034374 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -7.433034374 + -1.5
x = -7.433034374 + -1.5

Combine like terms: -7.433034374 + -1.5 = -8.933034374
x = -8.933034374

Simplifying
x = -8.933034374

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.933034374, -8.933034374}
Solution
x = {5.933034374, -8.933034374}