0=12w^2+12w-36

Solution for 0=12w^2+12w-36 equation:

Simplifying
0 = 12w2 + 12w + -36

Reorder the terms:
0 = -36 + 12w + 12w2

Solving
0 = -36 + 12w + 12w2

Solving for variable 'w'.

Combine like terms: 0 + 36 = 36
36 + -12w + -12w2 = -36 + 12w + 12w2 + 36 + -12w + -12w2

Reorder the terms:
36 + -12w + -12w2 = -36 + 36 + 12w + -12w + 12w2 + -12w2

Combine like terms: -36 + 36 = 0
36 + -12w + -12w2 = 0 + 12w + -12w + 12w2 + -12w2
36 + -12w + -12w2 = 12w + -12w + 12w2 + -12w2

Combine like terms: 12w + -12w = 0
36 + -12w + -12w2 = 0 + 12w2 + -12w2
36 + -12w + -12w2 = 12w2 + -12w2

Combine like terms: 12w2 + -12w2 = 0
36 + -12w + -12w2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(3 + -1w + -1w2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(3 + -1w + -1w2)' equal to zero and attempt to solve:

Simplifying
3 + -1w + -1w2 = 0

Solving
3 + -1w + -1w2 = 0

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

Divide each side by '-1'.
-3 + w + w2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + w + 3 + w2 = 0 + 3

Reorder the terms:
-3 + 3 + w + w2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + w + w2 = 0 + 3
w + w2 = 0 + 3

Combine like terms: 0 + 3 = 3
w + w2 = 3

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 = 3 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + w2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
1.25 + w2 = 3.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(w + 0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
w + 0.5 = 1.802775638

Simplifying
w + 0.5 = 1.802775638

Reorder the terms:
0.5 + w = 1.802775638

Solving
0.5 + w = 1.802775638

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 = 1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 1.802775638 + -0.5
w = 1.802775638 + -0.5

Combine like terms: 1.802775638 + -0.5 = 1.302775638
w = 1.302775638

Simplifying
w = 1.302775638

Subproblem 2
w + 0.5 = -1.802775638

Simplifying
w + 0.5 = -1.802775638

Reorder the terms:
0.5 + w = -1.802775638

Solving
0.5 + w = -1.802775638

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 = -1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -1.802775638 + -0.5
w = -1.802775638 + -0.5

Combine like terms: -1.802775638 + -0.5 = -2.302775638
w = -2.302775638

Simplifying
w = -2.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.302775638, -2.302775638}
Solution
w = {1.302775638, -2.302775638}