(2w^2-7w-6)+(4w^2-5w+1)=

Solution for (2w^2-7w-6)+(4w^2-5w+1)= equation:

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

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

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

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

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

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

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

Combine like terms: -7w + -5w = -12w
-5 + -12w + 2w2 + 4w2 = 0

Combine like terms: 2w2 + 4w2 = 6w2
-5 + -12w + 6w2 = 0

Solving
-5 + -12w + 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'.
-0.8333333333 + -2w + w2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -2w + 0.8333333333 + w2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -2w + w2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -2w + w2 = 0 + 0.8333333333
-2w + w2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-2w + w2 = 0.8333333333

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 = 0.8333333333 + 1

Reorder the terms:
1 + -2w + w2 = 0.8333333333 + 1

Combine like terms: 0.8333333333 + 1 = 1.8333333333
1 + -2w + w2 = 1.8333333333

Factor a perfect square on the left side:
(w + -1)(w + -1) = 1.8333333333

Calculate the square root of the right side: 1.354006401

Break this problem into two subproblems by setting 
(w + -1) equal to 1.354006401 and -1.354006401.

Subproblem 1
w + -1 = 1.354006401

Simplifying
w + -1 = 1.354006401

Reorder the terms:
-1 + w = 1.354006401

Solving
-1 + w = 1.354006401

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 = 1.354006401 + 1

Combine like terms: -1 + 1 = 0
0 + w = 1.354006401 + 1
w = 1.354006401 + 1

Combine like terms: 1.354006401 + 1 = 2.354006401
w = 2.354006401

Simplifying
w = 2.354006401

Subproblem 2
w + -1 = -1.354006401

Simplifying
w + -1 = -1.354006401

Reorder the terms:
-1 + w = -1.354006401

Solving
-1 + w = -1.354006401

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 = -1.354006401 + 1

Combine like terms: -1 + 1 = 0
0 + w = -1.354006401 + 1
w = -1.354006401 + 1

Combine like terms: -1.354006401 + 1 = -0.354006401
w = -0.354006401

Simplifying
w = -0.354006401

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.354006401, -0.354006401}