-6w^2=-(12w-4)

Solution for -6w^2=-(12w-4) equation:

Simplifying
-6w2 = -1(12w + -4)

Reorder the terms:
-6w2 = -1(-4 + 12w)
-6w2 = (-4 * -1 + 12w * -1)
-6w2 = (4 + -12w)

Solving
-6w2 = 4 + -12w

Solving for variable 'w'.

Reorder the terms:
-4 + 12w + -6w2 = 4 + -12w + -4 + 12w

Reorder the terms:
-4 + 12w + -6w2 = 4 + -4 + -12w + 12w

Combine like terms: 4 + -4 = 0
-4 + 12w + -6w2 = 0 + -12w + 12w
-4 + 12w + -6w2 = -12w + 12w

Combine like terms: -12w + 12w = 0
-4 + 12w + -6w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 6w + -3w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + 6w + -3w2)' equal to zero and attempt to solve:

Simplifying
-2 + 6w + -3w2 = 0

Solving
-2 + 6w + -3w2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.6666666667 + -2w + w2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -2w + -0.6666666667 + w2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -2w + w2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -2w + w2 = 0 + -0.6666666667
-2w + w2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-2w + w2 = -0.6666666667

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = -0.6666666667 + 1

Reorder the terms:
1 + -2w + w2 = -0.6666666667 + 1

Combine like terms: -0.6666666667 + 1 = 0.3333333333
1 + -2w + w2 = 0.3333333333

Factor a perfect square on the left side:
(w + -1)(w + -1) = 0.3333333333

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(w + -1) equal to 0.577350269 and -0.577350269.

Subproblem 1
w + -1 = 0.577350269

Simplifying
w + -1 = 0.577350269

Reorder the terms:
-1 + w = 0.577350269

Solving
-1 + w = 0.577350269

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = 0.577350269 + 1

Combine like terms: -1 + 1 = 0
0 + w = 0.577350269 + 1
w = 0.577350269 + 1

Combine like terms: 0.577350269 + 1 = 1.577350269
w = 1.577350269

Simplifying
w = 1.577350269

Subproblem 2
w + -1 = -0.577350269

Simplifying
w + -1 = -0.577350269

Reorder the terms:
-1 + w = -0.577350269

Solving
-1 + w = -0.577350269

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = -0.577350269 + 1

Combine like terms: -1 + 1 = 0
0 + w = -0.577350269 + 1
w = -0.577350269 + 1

Combine like terms: -0.577350269 + 1 = 0.422649731
w = 0.422649731

Simplifying
w = 0.422649731

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.577350269, 0.422649731}
Solution
w = {1.577350269, 0.422649731}