w^2=24-5w

Solution for w^2=24-5w equation:

Simplifying
w2 = 24 + -5w

Solving
w2 = 24 + -5w

Solving for variable 'w'.

Reorder the terms:
-24 + 5w + w2 = 24 + -5w + -24 + 5w

Reorder the terms:
-24 + 5w + w2 = 24 + -24 + -5w + 5w

Combine like terms: 24 + -24 = 0
-24 + 5w + w2 = 0 + -5w + 5w
-24 + 5w + w2 = -5w + 5w

Combine like terms: -5w + 5w = 0
-24 + 5w + w2 = 0

Factor a trinomial.
(-8 + -1w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-8 + -1w)' equal to zero and attempt to solve:

Simplifying
-8 + -1w = 0

Solving
-8 + -1w = 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 + -1w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1w = 0 + 8
-1w = 0 + 8

Combine like terms: 0 + 8 = 8
-1w = 8

Divide each side by '-1'.
w = -8

Simplifying
w = -8
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-8, 3}