36=2[(2w+3)(w)]

Solution for 36=2[(2w+3)(w)] equation:

Simplifying
36 = 2[(2w + 3)(w)]

Reorder the terms:
36 = 2[(3 + 2w)(w)]

Reorder the terms for easier multiplication:
36 = 2[w(3 + 2w)]
36 = 2[(3 * w + 2w * w)]
36 = 2[(3w + 2w2)]
36 = [3w * 2 + 2w2 * 2]
36 = [6w + 4w2]

Solving
36 = 6w + 4w2

Solving for variable 'w'.

Reorder the terms:
36 + -6w + -4w2 = 6w + -6w + 4w2 + -4w2

Combine like terms: 6w + -6w = 0
36 + -6w + -4w2 = 0 + 4w2 + -4w2
36 + -6w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
36 + -6w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -3w + -2w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(18 + -3w + -2w2)' equal to zero and attempt to solve:

Simplifying
18 + -3w + -2w2 = 0

Solving
18 + -3w + -2w2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-9 + 1.5w + w2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 1.5w + 9 + w2 = 0 + 9

Reorder the terms:
-9 + 9 + 1.5w + w2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 1.5w + w2 = 0 + 9
1.5w + w2 = 0 + 9

Combine like terms: 0 + 9 = 9
1.5w + w2 = 9

The w term is 1.5w.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5w + 0.5625 + w2 = 9 + 0.5625

Reorder the terms:
0.5625 + 1.5w + w2 = 9 + 0.5625

Combine like terms: 9 + 0.5625 = 9.5625
0.5625 + 1.5w + w2 = 9.5625

Factor a perfect square on the left side:
(w + 0.75)(w + 0.75) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(w + 0.75) equal to 3.092329219 and -3.092329219.

Subproblem 1
w + 0.75 = 3.092329219

Simplifying
w + 0.75 = 3.092329219

Reorder the terms:
0.75 + w = 3.092329219

Solving
0.75 + w = 3.092329219

Solving for variable 'w'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + w = 3.092329219 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + w = 3.092329219 + -0.75
w = 3.092329219 + -0.75

Combine like terms: 3.092329219 + -0.75 = 2.342329219
w = 2.342329219

Simplifying
w = 2.342329219

Subproblem 2
w + 0.75 = -3.092329219

Simplifying
w + 0.75 = -3.092329219

Reorder the terms:
0.75 + w = -3.092329219

Solving
0.75 + w = -3.092329219

Solving for variable 'w'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + w = -3.092329219 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + w = -3.092329219 + -0.75
w = -3.092329219 + -0.75

Combine like terms: -3.092329219 + -0.75 = -3.842329219
w = -3.842329219

Simplifying
w = -3.842329219

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.342329219, -3.842329219}
Solution
w = {2.342329219, -3.842329219}