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

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

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

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

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

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

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

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

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

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

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

Solving
3 + -2w + -1w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -1w)(3 + w) = 0

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 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 + -1w = 0 + -1

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

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

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

Simplifying
w = 1
Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
Solution
w = {1, -3}