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

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

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

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

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

Multiply (11 + w) * (-5 + w)
2(11(-5 + w) + w(-5 + w)) = 100
2((-5 * 11 + w * 11) + w(-5 + w)) = 100
2((-55 + 11w) + w(-5 + w)) = 100
2(-55 + 11w + (-5 * w + w * w)) = 100
2(-55 + 11w + (-5w + w2)) = 100

Combine like terms: 11w + -5w = 6w
2(-55 + 6w + w2) = 100
(-55 * 2 + 6w * 2 + w2 * 2) = 100
(-110 + 12w + 2w2) = 100

Solving
-110 + 12w + 2w2 = 100

Solving for variable 'w'.

Reorder the terms:
-110 + -100 + 12w + 2w2 = 100 + -100

Combine like terms: -110 + -100 = -210
-210 + 12w + 2w2 = 100 + -100

Combine like terms: 100 + -100 = 0
-210 + 12w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-105 + 6w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-105 + 6w + w2)' equal to zero and attempt to solve:

Simplifying
-105 + 6w + w2 = 0

Solving
-105 + 6w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 6w + 105 + w2 = 0 + 105

Reorder the terms:
-105 + 105 + 6w + w2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 6w + w2 = 0 + 105
6w + w2 = 0 + 105

Combine like terms: 0 + 105 = 105
6w + w2 = 105

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

Add '9' to each side of the equation.
6w + 9 + w2 = 105 + 9

Reorder the terms:
9 + 6w + w2 = 105 + 9

Combine like terms: 105 + 9 = 114
9 + 6w + w2 = 114

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

Calculate the square root of the right side: 10.677078252

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

Subproblem 1
w + 3 = 10.677078252

Simplifying
w + 3 = 10.677078252

Reorder the terms:
3 + w = 10.677078252

Solving
3 + w = 10.677078252

Solving for variable 'w'.

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

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

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

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

Simplifying
w = 7.677078252

Subproblem 2
w + 3 = -10.677078252

Simplifying
w + 3 = -10.677078252

Reorder the terms:
3 + w = -10.677078252

Solving
3 + w = -10.677078252

Solving for variable 'w'.

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

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

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

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

Simplifying
w = -13.677078252

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