w^2=-15-8w

Solution for w^2=-15-8w equation:

Simplifying
w2 = -15 + -8w

Solving
w2 = -15 + -8w

Solving for variable 'w'.

Reorder the terms:
15 + 8w + w2 = -15 + -8w + 15 + 8w

Reorder the terms:
15 + 8w + w2 = -15 + 15 + -8w + 8w

Combine like terms: -15 + 15 = 0
15 + 8w + w2 = 0 + -8w + 8w
15 + 8w + w2 = -8w + 8w

Combine like terms: -8w + 8w = 0
15 + 8w + w2 = 0

Factor a trinomial.
(5 + w)(3 + w) = 0

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

Simplifying
5 + w = 0

Solving
5 + w = 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 + w = 0 + -5

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

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

Simplifying
w = -5
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 = {-5, -3}