3r^2=-3r+90

Solution for 3r^2=-3r+90 equation:

Simplifying
3r2 = -3r + 90

Reorder the terms:
3r2 = 90 + -3r

Solving
3r2 = 90 + -3r

Solving for variable 'r'.

Reorder the terms:
-90 + 3r + 3r2 = 90 + -3r + -90 + 3r

Reorder the terms:
-90 + 3r + 3r2 = 90 + -90 + -3r + 3r

Combine like terms: 90 + -90 = 0
-90 + 3r + 3r2 = 0 + -3r + 3r
-90 + 3r + 3r2 = -3r + 3r

Combine like terms: -3r + 3r = 0
-90 + 3r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + r + r2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-6, 5}