6w^2+54w+120=0

Solution for 6w^2+54w+120=0 equation:

Simplifying
6w2 + 54w + 120 = 0

Reorder the terms:
120 + 54w + 6w2 = 0

Solving
120 + 54w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '6'.
6(20 + 9w + w2) = 0

Factor a trinomial.
6((5 + w)(4 + w)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

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

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

Simplifying
w = -5
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 = {-5, -4}