(y+12)y=-32

Solution for (y+12)y=-32 equation:

Simplifying
(y + 12) * y = -32

Reorder the terms:
(12 + y) * y = -32

Reorder the terms for easier multiplication:
y(12 + y) = -32
(12 * y + y * y) = -32
(12y + y2) = -32

Solving
12y + y2 = -32

Solving for variable 'y'.

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

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

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

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

Simplifying
8 + y = 0

Solving
8 + y = 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 + y = 0 + -8

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

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

Simplifying
y = -8
Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 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 + y = 0 + -4

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

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

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