2(x+9)(x-4)=110

Solution for 2(x+9)(x-4)=110 equation:

Simplifying
2(x + 9)(x + -4) = 110

Reorder the terms:
2(9 + x)(x + -4) = 110

Reorder the terms:
2(9 + x)(-4 + x) = 110

Multiply (9 + x) * (-4 + x)
2(9(-4 + x) + x(-4 + x)) = 110
2((-4 * 9 + x * 9) + x(-4 + x)) = 110
2((-36 + 9x) + x(-4 + x)) = 110
2(-36 + 9x + (-4 * x + x * x)) = 110
2(-36 + 9x + (-4x + x2)) = 110

Combine like terms: 9x + -4x = 5x
2(-36 + 5x + x2) = 110
(-36 * 2 + 5x * 2 + x2 * 2) = 110
(-72 + 10x + 2x2) = 110

Solving
-72 + 10x + 2x2 = 110

Solving for variable 'x'.

Reorder the terms:
-72 + -110 + 10x + 2x2 = 110 + -110

Combine like terms: -72 + -110 = -182
-182 + 10x + 2x2 = 110 + -110

Combine like terms: 110 + -110 = 0
-182 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-91 + 5x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-91 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-91 + 5x + x2 = 0

Solving
-91 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '91' to each side of the equation.
-91 + 5x + 91 + x2 = 0 + 91

Reorder the terms:
-91 + 91 + 5x + x2 = 0 + 91

Combine like terms: -91 + 91 = 0
0 + 5x + x2 = 0 + 91
5x + x2 = 0 + 91

Combine like terms: 0 + 91 = 91
5x + x2 = 91

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 91 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 91 + 6.25

Combine like terms: 91 + 6.25 = 97.25
6.25 + 5x + x2 = 97.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 97.25

Calculate the square root of the right side: 9.861541462

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.861541462 and -9.861541462.

Subproblem 1
x + 2.5 = 9.861541462

Simplifying
x + 2.5 = 9.861541462

Reorder the terms:
2.5 + x = 9.861541462

Solving
2.5 + x = 9.861541462

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 9.861541462 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.861541462 + -2.5
x = 9.861541462 + -2.5

Combine like terms: 9.861541462 + -2.5 = 7.361541462
x = 7.361541462

Simplifying
x = 7.361541462

Subproblem 2
x + 2.5 = -9.861541462

Simplifying
x + 2.5 = -9.861541462

Reorder the terms:
2.5 + x = -9.861541462

Solving
2.5 + x = -9.861541462

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -9.861541462 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.861541462 + -2.5
x = -9.861541462 + -2.5

Combine like terms: -9.861541462 + -2.5 = -12.361541462
x = -12.361541462

Simplifying
x = -12.361541462

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.361541462, -12.361541462}
Solution
x = {7.361541462, -12.361541462}