2y^2+12y=80

Solution for 2y^2+12y=80 equation:

Simplifying
2y2 + 12y = 80

Reorder the terms:
12y + 2y2 = 80

Solving
12y + 2y2 = 80

Solving for variable 'y'.

Reorder the terms:
-80 + 12y + 2y2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 12y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 6y + y2) = 0

Factor a trinomial.
2((-10 + -1y)(4 + -1y)) = 0

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

Simplifying
-10 + -1y = 0

Solving
-10 + -1y = 0

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

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

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

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

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

Simplifying
y = -10
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-10, 4}