y^2+12y-32=32

Solution for y^2+12y-32=32 equation:

Simplifying
y2 + 12y + -32 = 32

Reorder the terms:
-32 + 12y + y2 = 32

Solving
-32 + 12y + y2 = 32

Solving for variable 'y'.

Reorder the terms:
-32 + -32 + 12y + y2 = 32 + -32

Combine like terms: -32 + -32 = -64
-64 + 12y + y2 = 32 + -32

Combine like terms: 32 + -32 = 0
-64 + 12y + y2 = 0

Factor a trinomial.
(-16 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-16 + -1y)' equal to zero and attempt to solve:

Simplifying
-16 + -1y = 0

Solving
-16 + -1y = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1y = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1y = 0 + 16
-1y = 0 + 16

Combine like terms: 0 + 16 = 16
-1y = 16

Divide each side by '-1'.
y = -16

Simplifying
y = -16
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 = {-16, 4}