2y^2+14y=120

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

Simplifying
2y2 + 14y = 120

Reorder the terms:
14y + 2y2 = 120

Solving
14y + 2y2 = 120

Solving for variable 'y'.

Reorder the terms:
-120 + 14y + 2y2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 14y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + 7y + y2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -1y)' equal to zero and attempt to solve:

Simplifying
-12 + -1y = 0

Solving
-12 + -1y = 0

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

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

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

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

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

Simplifying
y = -12
Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

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

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

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

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