2w^2+8w=120

Solution for 2w^2+8w=120 equation:

Simplifying
2w2 + 8w = 120

Reorder the terms:
8w + 2w2 = 120

Solving
8w + 2w2 = 120

Solving for variable 'w'.

Reorder the terms:
-120 + 8w + 2w2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 8w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + 4w + w2) = 0

Factor a trinomial.
2((-10 + -1w)(6 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve:

Simplifying
-10 + -1w = 0

Solving
-10 + -1w = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1w = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1w = 0 + 10
-1w = 0 + 10

Combine like terms: 0 + 10 = 10
-1w = 10

Divide each side by '-1'.
w = -10

Simplifying
w = -10
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 = {-10, 6}