w^2=-27-12w

Solution for w^2=-27-12w equation:

Simplifying
w2 = -27 + -12w

Solving
w2 = -27 + -12w

Solving for variable 'w'.

Reorder the terms:
27 + 12w + w2 = -27 + -12w + 27 + 12w

Reorder the terms:
27 + 12w + w2 = -27 + 27 + -12w + 12w

Combine like terms: -27 + 27 = 0
27 + 12w + w2 = 0 + -12w + 12w
27 + 12w + w2 = -12w + 12w

Combine like terms: -12w + 12w = 0
27 + 12w + w2 = 0

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

Subproblem 1
Set the factor '(9 + w)' equal to zero and attempt to solve:

Simplifying
9 + w = 0

Solving
9 + w = 0

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

Add '-9' to each side of the equation.
9 + -9 + w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + w = 0 + -9
w = 0 + -9

Combine like terms: 0 + -9 = -9
w = -9

Simplifying
w = -9
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 = {-9, -3}