(-4w^2+6w-2)+(3w^2+5w+1)=

Solution for (-4w^2+6w-2)+(3w^2+5w+1)= equation:

Simplifying
(-4w2 + 6w + -2) + (3w2 + 5w + 1) = 0

Reorder the terms:
(-2 + 6w + -4w2) + (3w2 + 5w + 1) = 0

Remove parenthesis around (-2 + 6w + -4w2)
-2 + 6w + -4w2 + (3w2 + 5w + 1) = 0

Reorder the terms:
-2 + 6w + -4w2 + (1 + 5w + 3w2) = 0

Remove parenthesis around (1 + 5w + 3w2)
-2 + 6w + -4w2 + 1 + 5w + 3w2 = 0

Reorder the terms:
-2 + 1 + 6w + 5w + -4w2 + 3w2 = 0

Combine like terms: -2 + 1 = -1
-1 + 6w + 5w + -4w2 + 3w2 = 0

Combine like terms: 6w + 5w = 11w
-1 + 11w + -4w2 + 3w2 = 0

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

Solving
-1 + 11w + -1w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1 + -11w + w2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -11w + -1 + w2 = 0 + -1

Reorder the terms:
1 + -1 + -11w + w2 = 0 + -1

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

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

The w term is -11w.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11w + 30.25 + w2 = -1 + 30.25

Reorder the terms:
30.25 + -11w + w2 = -1 + 30.25

Combine like terms: -1 + 30.25 = 29.25
30.25 + -11w + w2 = 29.25

Factor a perfect square on the left side:
(w + -5.5)(w + -5.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(w + -5.5) equal to 5.408326913 and -5.408326913.

Subproblem 1
w + -5.5 = 5.408326913

Simplifying
w + -5.5 = 5.408326913

Reorder the terms:
-5.5 + w = 5.408326913

Solving
-5.5 + w = 5.408326913

Solving for variable 'w'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + w = 5.408326913 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + w = 5.408326913 + 5.5
w = 5.408326913 + 5.5

Combine like terms: 5.408326913 + 5.5 = 10.908326913
w = 10.908326913

Simplifying
w = 10.908326913

Subproblem 2
w + -5.5 = -5.408326913

Simplifying
w + -5.5 = -5.408326913

Reorder the terms:
-5.5 + w = -5.408326913

Solving
-5.5 + w = -5.408326913

Solving for variable 'w'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + w = -5.408326913 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + w = -5.408326913 + 5.5
w = -5.408326913 + 5.5

Combine like terms: -5.408326913 + 5.5 = 0.091673087
w = 0.091673087

Simplifying
w = 0.091673087

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.908326913, 0.091673087}