w^2=-18-9w

Solution for w^2=-18-9w equation:

Simplifying
w2 = -18 + -9w

Solving
w2 = -18 + -9w

Solving for variable 'w'.

Reorder the terms:
18 + 9w + w2 = -18 + -9w + 18 + 9w

Reorder the terms:
18 + 9w + w2 = -18 + 18 + -9w + 9w

Combine like terms: -18 + 18 = 0
18 + 9w + w2 = 0 + -9w + 9w
18 + 9w + w2 = -9w + 9w

Combine like terms: -9w + 9w = 0
18 + 9w + w2 = 0

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

Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
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 = {-6, -3}