3r^2-9r=30

Solution for 3r^2-9r=30 equation:

Simplifying
3r2 + -9r = 30

Reorder the terms:
-9r + 3r2 = 30

Solving
-9r + 3r2 = 30

Solving for variable 'r'.

Reorder the terms:
-30 + -9r + 3r2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -9r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -3r + r2) = 0

Factor a trinomial.
3((-2 + -1r)(5 + -1r)) = 0

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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

Simplifying
r = -2
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 = {-2, 5}