(w^2)+3w+-108=0

Solution for (w^2)+3w+-108=0 equation:

Simplifying
(w2) + 3w + -108 = 0
w2 + 3w + -108 = 0

Reorder the terms:
-108 + 3w + w2 = 0

Solving
-108 + 3w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-12 + -1w)(9 + -1w) = 0

Subproblem 1
Set the factor '(-12 + -1w)' equal to zero and attempt to solve:

Simplifying
-12 + -1w = 0

Solving
-12 + -1w = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1w = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1w = 0 + 12
-1w = 0 + 12

Combine like terms: 0 + 12 = 12
-1w = 12

Divide each side by '-1'.
w = -12

Simplifying
w = -12
Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {-12, 9}