-r^2+12r-32=0

Solution for -r^2+12r-32=0 equation:

Simplifying
-1r2 + 12r + -32 = 0

Reorder the terms:
-32 + 12r + -1r2 = 0

Solving
-32 + 12r + -1r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-8 + r)(4 + -1r) = 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 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 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 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

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