2w^2+14w=120

Solution for 2w^2+14w=120 equation:

Simplifying
2w2 + 14w = 120

Reorder the terms:
14w + 2w2 = 120

Solving
14w + 2w2 = 120

Solving for variable 'w'.

Reorder the terms:
-120 + 14w + 2w2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 14w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + 7w + w2) = 0

Factor a trinomial.
2((-12 + -1w)(5 + -1w)) = 0

Ignore the factor 2.
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 '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 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 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-12, 5}