0=2(w^2+w-36)

Solution for 0=2(w^2+w-36) equation:

Simplifying
0 = 2(w2 + w + -36)

Reorder the terms:
0 = 2(-36 + w + w2)
0 = (-36 * 2 + w * 2 + w2 * 2)
0 = (-72 + 2w + 2w2)

Solving
0 = -72 + 2w + 2w2

Solving for variable 'w'.

Combine like terms: 0 + 72 = 72
72 + -2w + -2w2 = -72 + 2w + 2w2 + 72 + -2w + -2w2

Reorder the terms:
72 + -2w + -2w2 = -72 + 72 + 2w + -2w + 2w2 + -2w2

Combine like terms: -72 + 72 = 0
72 + -2w + -2w2 = 0 + 2w + -2w + 2w2 + -2w2
72 + -2w + -2w2 = 2w + -2w + 2w2 + -2w2

Combine like terms: 2w + -2w = 0
72 + -2w + -2w2 = 0 + 2w2 + -2w2
72 + -2w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
72 + -2w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -1w + -1w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(36 + -1w + -1w2)' equal to zero and attempt to solve:

Simplifying
36 + -1w + -1w2 = 0

Solving
36 + -1w + -1w2 = 0

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

Divide each side by '-1'.
-36 + w + w2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + w + 36 + w2 = 0 + 36

Reorder the terms:
-36 + 36 + w + w2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + w + w2 = 0 + 36
w + w2 = 0 + 36

Combine like terms: 0 + 36 = 36
w + w2 = 36

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + w2 = 36 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + w2 = 36 + 0.25

Combine like terms: 36 + 0.25 = 36.25
1.25 + w2 = 36.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(w + 0.5) equal to 6.020797289 and -6.020797289.

Subproblem 1
w + 0.5 = 6.020797289

Simplifying
w + 0.5 = 6.020797289

Reorder the terms:
0.5 + w = 6.020797289

Solving
0.5 + w = 6.020797289

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 6.020797289 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 6.020797289 + -0.5
w = 6.020797289 + -0.5

Combine like terms: 6.020797289 + -0.5 = 5.520797289
w = 5.520797289

Simplifying
w = 5.520797289

Subproblem 2
w + 0.5 = -6.020797289

Simplifying
w + 0.5 = -6.020797289

Reorder the terms:
0.5 + w = -6.020797289

Solving
0.5 + w = -6.020797289

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -6.020797289 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -6.020797289 + -0.5
w = -6.020797289 + -0.5

Combine like terms: -6.020797289 + -0.5 = -6.520797289
w = -6.520797289

Simplifying
w = -6.520797289

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.520797289, -6.520797289}
Solution
w = {5.520797289, -6.520797289}