(2w^2-5w+6)-(-3w^2+w+7)=

Solution for (2w^2-5w+6)-(-3w^2+w+7)= equation:

Simplifying
(2w2 + -5w + 6) + -1(-3w2 + w + 7) = 0

Reorder the terms:
(6 + -5w + 2w2) + -1(-3w2 + w + 7) = 0

Remove parenthesis around (6 + -5w + 2w2)
6 + -5w + 2w2 + -1(-3w2 + w + 7) = 0

Reorder the terms:
6 + -5w + 2w2 + -1(7 + w + -3w2) = 0
6 + -5w + 2w2 + (7 * -1 + w * -1 + -3w2 * -1) = 0
6 + -5w + 2w2 + (-7 + -1w + 3w2) = 0

Reorder the terms:
6 + -7 + -5w + -1w + 2w2 + 3w2 = 0

Combine like terms: 6 + -7 = -1
-1 + -5w + -1w + 2w2 + 3w2 = 0

Combine like terms: -5w + -1w = -6w
-1 + -6w + 2w2 + 3w2 = 0

Combine like terms: 2w2 + 3w2 = 5w2
-1 + -6w + 5w2 = 0

Solving
-1 + -6w + 5w2 = 0

Solving for variable 'w'.

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

Divide each side by '5'.
-0.2 + -1.2w + w2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -1.2w + 0.2 + w2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -1.2w + w2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -1.2w + w2 = 0 + 0.2
-1.2w + w2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-1.2w + w2 = 0.2

The w term is -1.2w.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2w + 0.36 + w2 = 0.2 + 0.36

Reorder the terms:
0.36 + -1.2w + w2 = 0.2 + 0.36

Combine like terms: 0.2 + 0.36 = 0.56
0.36 + -1.2w + w2 = 0.56

Factor a perfect square on the left side:
(w + -0.6)(w + -0.6) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(w + -0.6) equal to 0.748331477 and -0.748331477.

Subproblem 1
w + -0.6 = 0.748331477

Simplifying
w + -0.6 = 0.748331477

Reorder the terms:
-0.6 + w = 0.748331477

Solving
-0.6 + w = 0.748331477

Solving for variable 'w'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + w = 0.748331477 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + w = 0.748331477 + 0.6
w = 0.748331477 + 0.6

Combine like terms: 0.748331477 + 0.6 = 1.348331477
w = 1.348331477

Simplifying
w = 1.348331477

Subproblem 2
w + -0.6 = -0.748331477

Simplifying
w + -0.6 = -0.748331477

Reorder the terms:
-0.6 + w = -0.748331477

Solving
-0.6 + w = -0.748331477

Solving for variable 'w'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + w = -0.748331477 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + w = -0.748331477 + 0.6
w = -0.748331477 + 0.6

Combine like terms: -0.748331477 + 0.6 = -0.148331477
w = -0.148331477

Simplifying
w = -0.148331477

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.348331477, -0.148331477}