w^2=-24-11w

Solution for w^2=-24-11w equation:

Simplifying
w2 = -24 + -11w

Solving
w2 = -24 + -11w

Solving for variable 'w'.

Reorder the terms:
24 + 11w + w2 = -24 + -11w + 24 + 11w

Reorder the terms:
24 + 11w + w2 = -24 + 24 + -11w + 11w

Combine like terms: -24 + 24 = 0
24 + 11w + w2 = 0 + -11w + 11w
24 + 11w + w2 = -11w + 11w

Combine like terms: -11w + 11w = 0
24 + 11w + w2 = 0

Factor a trinomial.
(8 + w)(3 + 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 '(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 = {-8, -3}