(y+4)y=32

Solution for (y+4)y=32 equation:

Simplifying
(y + 4) * y = 32

Reorder the terms:
(4 + y) * y = 32

Reorder the terms for easier multiplication:
y(4 + y) = 32
(4 * y + y * y) = 32
(4y + y2) = 32

Solving
4y + y2 = 32

Solving for variable 'y'.

Reorder the terms:
-32 + 4y + y2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 4y + y2 = 0

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

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}