w^2=-12-7w

Solution for w^2=-12-7w equation:

Simplifying
w2 = -12 + -7w

Solving
w2 = -12 + -7w

Solving for variable 'w'.

Reorder the terms:
12 + 7w + w2 = -12 + -7w + 12 + 7w

Reorder the terms:
12 + 7w + w2 = -12 + 12 + -7w + 7w

Combine like terms: -12 + 12 = 0
12 + 7w + w2 = 0 + -7w + 7w
12 + 7w + w2 = -7w + 7w

Combine like terms: -7w + 7w = 0
12 + 7w + w2 = 0

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

Subproblem 1
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
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 = {-4, -3}