2w^2+7w=-5

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

Simplifying
2w2 + 7w = -5

Reorder the terms:
7w + 2w2 = -5

Solving
7w + 2w2 = -5

Solving for variable 'w'.

Reorder the terms:
5 + 7w + 2w2 = -5 + 5

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

Factor a trinomial.
(5 + 2w)(1 + w) = 0

Subproblem 1
Set the factor '(5 + 2w)' equal to zero and attempt to solve:

Simplifying
5 + 2w = 0

Solving
5 + 2w = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2w = 0 + -5
2w = 0 + -5

Combine like terms: 0 + -5 = -5
2w = -5

Divide each side by '2'.
w = -2.5

Simplifying
w = -2.5
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 = {-2.5, -1}