(2w^2-7w-6)-(8w^2+4w-4)=

Solution for (2w^2-7w-6)-(8w^2+4w-4)= equation:

Simplifying
(2w2 + -7w + -6) + -1(8w2 + 4w + -4) = 0

Reorder the terms:
(-6 + -7w + 2w2) + -1(8w2 + 4w + -4) = 0

Remove parenthesis around (-6 + -7w + 2w2)
-6 + -7w + 2w2 + -1(8w2 + 4w + -4) = 0

Reorder the terms:
-6 + -7w + 2w2 + -1(-4 + 4w + 8w2) = 0
-6 + -7w + 2w2 + (-4 * -1 + 4w * -1 + 8w2 * -1) = 0
-6 + -7w + 2w2 + (4 + -4w + -8w2) = 0

Reorder the terms:
-6 + 4 + -7w + -4w + 2w2 + -8w2 = 0

Combine like terms: -6 + 4 = -2
-2 + -7w + -4w + 2w2 + -8w2 = 0

Combine like terms: -7w + -4w = -11w
-2 + -11w + 2w2 + -8w2 = 0

Combine like terms: 2w2 + -8w2 = -6w2
-2 + -11w + -6w2 = 0

Solving
-2 + -11w + -6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 11w + 6w2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 11w + 6w2)' equal to zero and attempt to solve:

Simplifying
2 + 11w + 6w2 = 0

Solving
2 + 11w + 6w2 = 0

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

Divide each side by '6'.
0.3333333333 + 1.833333333w + w2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 1.833333333w + -0.3333333333 + w2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 1.833333333w + w2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 1.833333333w + w2 = 0 + -0.3333333333
1.833333333w + w2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
1.833333333w + w2 = -0.3333333333

The w term is 1.833333333w.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333w + 0.8402777775 + w2 = -0.3333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333w + w2 = -0.3333333333 + 0.8402777775

Combine like terms: -0.3333333333 + 0.8402777775 = 0.5069444442
0.8402777775 + 1.833333333w + w2 = 0.5069444442

Factor a perfect square on the left side:
(w + 0.9166666665)(w + 0.9166666665) = 0.5069444442

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(w + 0.9166666665) equal to 0.712000312 and -0.712000312.

Subproblem 1
w + 0.9166666665 = 0.712000312

Simplifying
w + 0.9166666665 = 0.712000312

Reorder the terms:
0.9166666665 + w = 0.712000312

Solving
0.9166666665 + w = 0.712000312

Solving for variable 'w'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + w = 0.712000312 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + w = 0.712000312 + -0.9166666665
w = 0.712000312 + -0.9166666665

Combine like terms: 0.712000312 + -0.9166666665 = -0.2046663545
w = -0.2046663545

Simplifying
w = -0.2046663545

Subproblem 2
w + 0.9166666665 = -0.712000312

Simplifying
w + 0.9166666665 = -0.712000312

Reorder the terms:
0.9166666665 + w = -0.712000312

Solving
0.9166666665 + w = -0.712000312

Solving for variable 'w'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + w = -0.712000312 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + w = -0.712000312 + -0.9166666665
w = -0.712000312 + -0.9166666665

Combine like terms: -0.712000312 + -0.9166666665 = -1.6286669785
w = -1.6286669785

Simplifying
w = -1.6286669785

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.2046663545, -1.6286669785}
Solution
w = {-0.2046663545, -1.6286669785}