5w^2+7w+2-w^2+3w+4=

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

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

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

Combine like terms: 2 + 4 = 6
6 + 7w + 3w + 5w2 + -1w2 = 0

Combine like terms: 7w + 3w = 10w
6 + 10w + 5w2 + -1w2 = 0

Combine like terms: 5w2 + -1w2 = 4w2
6 + 10w + 4w2 = 0

Solving
6 + 10w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5w + 2w2) = 0

Factor a trinomial.
2((3 + 2w)(1 + w)) = 0

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

Simplifying
3 + 2w = 0

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

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
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 = {-1.5, -1}