3r^2-9r-390=0

Solution for 3r^2-9r-390=0 equation:

Simplifying
3r2 + -9r + -390 = 0

Reorder the terms:
-390 + -9r + 3r2 = 0

Solving
-390 + -9r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-130 + -3r + r2) = 0

Factor a trinomial.
3((-10 + -1r)(13 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -1r)' equal to zero and attempt to solve:

Simplifying
-10 + -1r = 0

Solving
-10 + -1r = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1r = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1r = 0 + 10
-1r = 0 + 10

Combine like terms: 0 + 10 = 10
-1r = 10

Divide each side by '-1'.
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(13 + -1r)' equal to zero and attempt to solve:

Simplifying
13 + -1r = 0

Solving
13 + -1r = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1r = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1r = 0 + -13
-1r = 0 + -13

Combine like terms: 0 + -13 = -13
-1r = -13

Divide each side by '-1'.
r = 13

Simplifying
r = 13
Solution
r = {-10, 13}