2y^2+8y+16=80

Solution for 2y^2+8y+16=80 equation:

Simplifying
2y2 + 8y + 16 = 80

Reorder the terms:
16 + 8y + 2y2 = 80

Solving
16 + 8y + 2y2 = 80

Solving for variable 'y'.

Reorder the terms:
16 + -80 + 8y + 2y2 = 80 + -80

Combine like terms: 16 + -80 = -64
-64 + 8y + 2y2 = 80 + -80

Combine like terms: 80 + -80 = 0
-64 + 8y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 4y + y2) = 0

Factor a trinomial.
2((-8 + -1y)(4 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8
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 = {-8, 4}