w^2=-24-10w

Solution for w^2=-24-10w equation:

Simplifying
w2 = -24 + -10w

Solving
w2 = -24 + -10w

Solving for variable 'w'.

Reorder the terms:
24 + 10w + w2 = -24 + -10w + 24 + 10w

Reorder the terms:
24 + 10w + w2 = -24 + 24 + -10w + 10w

Combine like terms: -24 + 24 = 0
24 + 10w + w2 = 0 + -10w + 10w
24 + 10w + w2 = -10w + 10w

Combine like terms: -10w + 10w = 0
24 + 10w + w2 = 0

Factor a trinomial.
(6 + w)(4 + 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 '(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 = {-6, -4}