(2w^2+4w^2-4)+(-2w^2-4w^2-7)-(-6w^2-5w+5)=

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Solution for (2w^2+4w^2-4)+(-2w^2-4w^2-7)-(-6w^2-5w+5)= equation: 


Simplifying
(2w2 + 4w2 + -4) + (-2w2 + -4w2 + -7) + -1(-6w2 + -5w + 5) = 0

Reorder the terms:
(-4 + 2w2 + 4w2) + (-2w2 + -4w2 + -7) + -1(-6w2 + -5w + 5) = 0

Combine like terms: 2w2 + 4w2 = 6w2
(-4 + 6w2) + (-2w2 + -4w2 + -7) + -1(-6w2 + -5w + 5) = 0

Remove parenthesis around (-4 + 6w2)
-4 + 6w2 + (-2w2 + -4w2 + -7) + -1(-6w2 + -5w + 5) = 0

Reorder the terms:
-4 + 6w2 + (-7 + -2w2 + -4w2) + -1(-6w2 + -5w + 5) = 0

Combine like terms: -2w2 + -4w2 = -6w2
-4 + 6w2 + (-7 + -6w2) + -1(-6w2 + -5w + 5) = 0

Remove parenthesis around (-7 + -6w2)
-4 + 6w2 + -7 + -6w2 + -1(-6w2 + -5w + 5) = 0

Reorder the terms:
-4 + 6w2 + -7 + -6w2 + -1(5 + -5w + -6w2) = 0
-4 + 6w2 + -7 + -6w2 + (5 * -1 + -5w * -1 + -6w2 * -1) = 0
-4 + 6w2 + -7 + -6w2 + (-5 + 5w + 6w2) = 0

Reorder the terms:
-4 + -7 + -5 + 5w + 6w2 + -6w2 + 6w2 = 0

Combine like terms: -4 + -7 = -11
-11 + -5 + 5w + 6w2 + -6w2 + 6w2 = 0

Combine like terms: -11 + -5 = -16
-16 + 5w + 6w2 + -6w2 + 6w2 = 0

Combine like terms: 6w2 + -6w2 = 0
-16 + 5w + 0 + 6w2 = 0
-16 + 5w + 6w2 = 0

Solving
-16 + 5w + 6w2 = 0

Solving for variable 'w'.

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

Divide each side by '6'.
-2.666666667 + 0.8333333333w + w2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 0.8333333333w + 2.666666667 + w2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 0.8333333333w + w2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 0.8333333333w + w2 = 0 + 2.666666667
0.8333333333w + w2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
0.8333333333w + w2 = 2.666666667

The w term is 0.8333333333w.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333w + 0.1736111111 + w2 = 2.666666667 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333w + w2 = 2.666666667 + 0.1736111111

Combine like terms: 2.666666667 + 0.1736111111 = 2.8402777781
0.1736111111 + 0.8333333333w + w2 = 2.8402777781

Factor a perfect square on the left side:
(w + 0.4166666667)(w + 0.4166666667) = 2.8402777781

Calculate the square root of the right side: 1.685312368

Break this problem into two subproblems by setting 
(w + 0.4166666667) equal to 1.685312368 and -1.685312368.


Subproblem 1
w + 0.4166666667 = 1.685312368

Simplifying
w + 0.4166666667 = 1.685312368

Reorder the terms:
0.4166666667 + w = 1.685312368

Solving
0.4166666667 + w = 1.685312368

Solving for variable 'w'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + w = 1.685312368 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + w = 1.685312368 + -0.4166666667
w = 1.685312368 + -0.4166666667

Combine like terms: 1.685312368 + -0.4166666667 = 1.2686457013
w = 1.2686457013

Simplifying
w = 1.2686457013


Subproblem 2
w + 0.4166666667 = -1.685312368

Simplifying
w + 0.4166666667 = -1.685312368

Reorder the terms:
0.4166666667 + w = -1.685312368

Solving
0.4166666667 + w = -1.685312368

Solving for variable 'w'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + w = -1.685312368 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + w = -1.685312368 + -0.4166666667
w = -1.685312368 + -0.4166666667

Combine like terms: -1.685312368 + -0.4166666667 = -2.1019790347
w = -2.1019790347

Simplifying
w = -2.1019790347


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.2686457013, -2.1019790347}

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