100=2(x+11)(x-5)

Solution for 100=2(x+11)(x-5) equation:

Simplifying
100 = 2(x + 11)(x + -5)

Reorder the terms:
100 = 2(11 + x)(x + -5)

Reorder the terms:
100 = 2(11 + x)(-5 + x)

Multiply (11 + x) * (-5 + x)
100 = 2(11(-5 + x) + x(-5 + x))
100 = 2((-5 * 11 + x * 11) + x(-5 + x))
100 = 2((-55 + 11x) + x(-5 + x))
100 = 2(-55 + 11x + (-5 * x + x * x))
100 = 2(-55 + 11x + (-5x + x2))

Combine like terms: 11x + -5x = 6x
100 = 2(-55 + 6x + x2)
100 = (-55 * 2 + 6x * 2 + x2 * 2)
100 = (-110 + 12x + 2x2)

Solving
100 = -110 + 12x + 2x2

Solving for variable 'x'.

Combine like terms: 100 + 110 = 210
210 + -12x + -2x2 = -110 + 12x + 2x2 + 110 + -12x + -2x2

Reorder the terms:
210 + -12x + -2x2 = -110 + 110 + 12x + -12x + 2x2 + -2x2

Combine like terms: -110 + 110 = 0
210 + -12x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2
210 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
210 + -12x + -2x2 = 0 + 2x2 + -2x2
210 + -12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
210 + -12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(105 + -6x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(105 + -6x + -1x2)' equal to zero and attempt to solve:

Simplifying
105 + -6x + -1x2 = 0

Solving
105 + -6x + -1x2 = 0

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

Divide each side by '-1'.
-105 + 6x + x2 = 0

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 6x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 6x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 6x + x2 = 0 + 105
6x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
6x + x2 = 105

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 105 + 9

Reorder the terms:
9 + 6x + x2 = 105 + 9

Combine like terms: 105 + 9 = 114
9 + 6x + x2 = 114

Factor a perfect square on the left side:
(x + 3)(x + 3) = 114

Calculate the square root of the right side: 10.677078252

Break this problem into two subproblems by setting 
(x + 3) equal to 10.677078252 and -10.677078252.

Subproblem 1
x + 3 = 10.677078252

Simplifying
x + 3 = 10.677078252

Reorder the terms:
3 + x = 10.677078252

Solving
3 + x = 10.677078252

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 10.677078252 + -3

Combine like terms: 3 + -3 = 0
0 + x = 10.677078252 + -3
x = 10.677078252 + -3

Combine like terms: 10.677078252 + -3 = 7.677078252
x = 7.677078252

Simplifying
x = 7.677078252

Subproblem 2
x + 3 = -10.677078252

Simplifying
x + 3 = -10.677078252

Reorder the terms:
3 + x = -10.677078252

Solving
3 + x = -10.677078252

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -10.677078252 + -3

Combine like terms: 3 + -3 = 0
0 + x = -10.677078252 + -3
x = -10.677078252 + -3

Combine like terms: -10.677078252 + -3 = -13.677078252
x = -13.677078252

Simplifying
x = -13.677078252

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.677078252, -13.677078252}
Solution
x = {7.677078252, -13.677078252}