12r=-r^2-32

Solution for 12r=-r^2-32 equation:

Simplifying
12r = -1r2 + -32

Reorder the terms:
12r = -32 + -1r2

Solving
12r = -32 + -1r2

Solving for variable 'r'.

Reorder the terms:
32 + 12r + r2 = -32 + -1r2 + 32 + r2

Reorder the terms:
32 + 12r + r2 = -32 + 32 + -1r2 + r2

Combine like terms: -32 + 32 = 0
32 + 12r + r2 = 0 + -1r2 + r2
32 + 12r + r2 = -1r2 + r2

Combine like terms: -1r2 + r2 = 0
32 + 12r + r2 = 0

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

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

Simplifying
8 + r = 0

Solving
8 + r = 0

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

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

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

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

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

Simplifying
4 + r = 0

Solving
4 + r = 0

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

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

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

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

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