w^2=-32-12w

Solution for w^2=-32-12w equation:

Simplifying
w2 = -32 + -12w

Solving
w2 = -32 + -12w

Solving for variable 'w'.

Reorder the terms:
32 + 12w + w2 = -32 + -12w + 32 + 12w

Reorder the terms:
32 + 12w + w2 = -32 + 32 + -12w + 12w

Combine like terms: -32 + 32 = 0
32 + 12w + w2 = 0 + -12w + 12w
32 + 12w + w2 = -12w + 12w

Combine like terms: -12w + 12w = 0
32 + 12w + w2 = 0

Factor a trinomial.
(8 + w)(4 + w) = 0

Subproblem 1
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

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

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

Simplifying
w = -8
Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 0

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

Add '-4' to each side of the equation.
4 + -4 + w = 0 + -4

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

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

Simplifying
w = -4
Solution
w = {-8, -4}