(2w^2-5w+3)+(-4w^2+7w+1)=

Solution for (2w^2-5w+3)+(-4w^2+7w+1)= equation:

Simplifying
(2w2 + -5w + 3) + (-4w2 + 7w + 1) = 0

Reorder the terms:
(3 + -5w + 2w2) + (-4w2 + 7w + 1) = 0

Remove parenthesis around (3 + -5w + 2w2)
3 + -5w + 2w2 + (-4w2 + 7w + 1) = 0

Reorder the terms:
3 + -5w + 2w2 + (1 + 7w + -4w2) = 0

Remove parenthesis around (1 + 7w + -4w2)
3 + -5w + 2w2 + 1 + 7w + -4w2 = 0

Reorder the terms:
3 + 1 + -5w + 7w + 2w2 + -4w2 = 0

Combine like terms: 3 + 1 = 4
4 + -5w + 7w + 2w2 + -4w2 = 0

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

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

Solving
4 + 2w + -2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + w + -1w2) = 0

Factor a trinomial.
2((2 + -1w)(1 + w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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 = 0 + -1

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

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

Simplifying
w = -1
Solution
w = {2, -1}