(w^2-7w+6)-(-3w^2+4w+5)=

Solution for (w^2-7w+6)-(-3w^2+4w+5)= equation:

Simplifying
(w2 + -7w + 6) + -1(-3w2 + 4w + 5) = 0

Reorder the terms:
(6 + -7w + w2) + -1(-3w2 + 4w + 5) = 0

Remove parenthesis around (6 + -7w + w2)
6 + -7w + w2 + -1(-3w2 + 4w + 5) = 0

Reorder the terms:
6 + -7w + w2 + -1(5 + 4w + -3w2) = 0
6 + -7w + w2 + (5 * -1 + 4w * -1 + -3w2 * -1) = 0
6 + -7w + w2 + (-5 + -4w + 3w2) = 0

Reorder the terms:
6 + -5 + -7w + -4w + w2 + 3w2 = 0

Combine like terms: 6 + -5 = 1
1 + -7w + -4w + w2 + 3w2 = 0

Combine like terms: -7w + -4w = -11w
1 + -11w + w2 + 3w2 = 0

Combine like terms: w2 + 3w2 = 4w2
1 + -11w + 4w2 = 0

Solving
1 + -11w + 4w2 = 0

Solving for variable 'w'.

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

Divide each side by '4'.
0.25 + -2.75w + w2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -2.75w + -0.25 + w2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -2.75w + w2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -2.75w + w2 = 0 + -0.25
-2.75w + w2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-2.75w + w2 = -0.25

The w term is -2.75w.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75w + 1.890625 + w2 = -0.25 + 1.890625

Reorder the terms:
1.890625 + -2.75w + w2 = -0.25 + 1.890625

Combine like terms: -0.25 + 1.890625 = 1.640625
1.890625 + -2.75w + w2 = 1.640625

Factor a perfect square on the left side:
(w + -1.375)(w + -1.375) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(w + -1.375) equal to 1.280868846 and -1.280868846.

Subproblem 1
w + -1.375 = 1.280868846

Simplifying
w + -1.375 = 1.280868846

Reorder the terms:
-1.375 + w = 1.280868846

Solving
-1.375 + w = 1.280868846

Solving for variable 'w'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + w = 1.280868846 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + w = 1.280868846 + 1.375
w = 1.280868846 + 1.375

Combine like terms: 1.280868846 + 1.375 = 2.655868846
w = 2.655868846

Simplifying
w = 2.655868846

Subproblem 2
w + -1.375 = -1.280868846

Simplifying
w + -1.375 = -1.280868846

Reorder the terms:
-1.375 + w = -1.280868846

Solving
-1.375 + w = -1.280868846

Solving for variable 'w'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + w = -1.280868846 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + w = -1.280868846 + 1.375
w = -1.280868846 + 1.375

Combine like terms: -1.280868846 + 1.375 = 0.094131154
w = 0.094131154

Simplifying
w = 0.094131154

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.655868846, 0.094131154}