w^2+24w-180=0

Solution for w^2+24w-180=0 equation:

Simplifying
w2 + 24w + -180 = 0

Reorder the terms:
-180 + 24w + w2 = 0

Solving
-180 + 24w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-30 + -1w)(6 + -1w) = 0

Subproblem 1
Set the factor '(-30 + -1w)' equal to zero and attempt to solve:

Simplifying
-30 + -1w = 0

Solving
-30 + -1w = 0

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

Add '30' to each side of the equation.
-30 + 30 + -1w = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1w = 0 + 30
-1w = 0 + 30

Combine like terms: 0 + 30 = 30
-1w = 30

Divide each side by '-1'.
w = -30

Simplifying
w = -30
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 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 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {-30, 6}