(3w^2-6w-6)=(4w^2+3w-3)

Solution for (3w^2-6w-6)=(4w^2+3w-3) equation:

Simplifying
(3w2 + -6w + -6) = (4w2 + 3w + -3)

Reorder the terms:
(-6 + -6w + 3w2) = (4w2 + 3w + -3)

Remove parenthesis around (-6 + -6w + 3w2)
-6 + -6w + 3w2 = (4w2 + 3w + -3)

Reorder the terms:
-6 + -6w + 3w2 = (-3 + 3w + 4w2)

Remove parenthesis around (-3 + 3w + 4w2)
-6 + -6w + 3w2 = -3 + 3w + 4w2

Solving
-6 + -6w + 3w2 = -3 + 3w + 4w2

Solving for variable 'w'.

Reorder the terms:
-6 + 3 + -6w + -3w + 3w2 + -4w2 = -3 + 3w + 4w2 + 3 + -3w + -4w2

Combine like terms: -6 + 3 = -3
-3 + -6w + -3w + 3w2 + -4w2 = -3 + 3w + 4w2 + 3 + -3w + -4w2

Combine like terms: -6w + -3w = -9w
-3 + -9w + 3w2 + -4w2 = -3 + 3w + 4w2 + 3 + -3w + -4w2

Combine like terms: 3w2 + -4w2 = -1w2
-3 + -9w + -1w2 = -3 + 3w + 4w2 + 3 + -3w + -4w2

Reorder the terms:
-3 + -9w + -1w2 = -3 + 3 + 3w + -3w + 4w2 + -4w2

Combine like terms: -3 + 3 = 0
-3 + -9w + -1w2 = 0 + 3w + -3w + 4w2 + -4w2
-3 + -9w + -1w2 = 3w + -3w + 4w2 + -4w2

Combine like terms: 3w + -3w = 0
-3 + -9w + -1w2 = 0 + 4w2 + -4w2
-3 + -9w + -1w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
-3 + -9w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 9w + w2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 9w + w2)' equal to zero and attempt to solve:

Simplifying
3 + 9w + w2 = 0

Solving
3 + 9w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 9w + -3 + w2 = 0 + -3

Reorder the terms:
3 + -3 + 9w + w2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 9w + w2 = 0 + -3
9w + w2 = 0 + -3

Combine like terms: 0 + -3 = -3
9w + w2 = -3

The w term is 9w.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9w + 20.25 + w2 = -3 + 20.25

Reorder the terms:
20.25 + 9w + w2 = -3 + 20.25

Combine like terms: -3 + 20.25 = 17.25
20.25 + 9w + w2 = 17.25

Factor a perfect square on the left side:
(w + 4.5)(w + 4.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(w + 4.5) equal to 4.153311931 and -4.153311931.

Subproblem 1
w + 4.5 = 4.153311931

Simplifying
w + 4.5 = 4.153311931

Reorder the terms:
4.5 + w = 4.153311931

Solving
4.5 + w = 4.153311931

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = 4.153311931 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = 4.153311931 + -4.5
w = 4.153311931 + -4.5

Combine like terms: 4.153311931 + -4.5 = -0.346688069
w = -0.346688069

Simplifying
w = -0.346688069

Subproblem 2
w + 4.5 = -4.153311931

Simplifying
w + 4.5 = -4.153311931

Reorder the terms:
4.5 + w = -4.153311931

Solving
4.5 + w = -4.153311931

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = -4.153311931 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = -4.153311931 + -4.5
w = -4.153311931 + -4.5

Combine like terms: -4.153311931 + -4.5 = -8.653311931
w = -8.653311931

Simplifying
w = -8.653311931

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.346688069, -8.653311931}
Solution
w = {-0.346688069, -8.653311931}