-90=15r-5r^2

Solution for -90=15r-5r^2 equation:

Simplifying
-90 = 15r + -5r2

Solving
-90 = 15r + -5r2

Solving for variable 'r'.

Reorder the terms:
-90 + -15r + 5r2 = 15r + -15r + -5r2 + 5r2

Combine like terms: 15r + -15r = 0
-90 + -15r + 5r2 = 0 + -5r2 + 5r2
-90 + -15r + 5r2 = -5r2 + 5r2

Combine like terms: -5r2 + 5r2 = 0
-90 + -15r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + -3r + r2) = 0

Factor a trinomial.
5((-3 + -1r)(6 + -1r)) = 0

Ignore the factor 5.
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 '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-3, 6}