-r^2-12r+45=

Solution for -r^2-12r+45= equation:

Simplifying
-1r2 + -12r + 45 = 0

Reorder the terms:
45 + -12r + -1r2 = 0

Solving
45 + -12r + -1r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -1r)(15 + r) = 0

Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
Set the factor '(15 + r)' equal to zero and attempt to solve:

Simplifying
15 + r = 0

Solving
15 + r = 0

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

Add '-15' to each side of the equation.
15 + -15 + r = 0 + -15

Combine like terms: 15 + -15 = 0
0 + r = 0 + -15
r = 0 + -15

Combine like terms: 0 + -15 = -15
r = -15

Simplifying
r = -15
Solution
r = {3, -15}