3r^2-9r-162=0

Solution for 3r^2-9r-162=0 equation:

Simplifying
3r2 + -9r + -162 = 0

Reorder the terms:
-162 + -9r + 3r2 = 0

Solving
-162 + -9r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-54 + -3r + r2) = 0

Factor a trinomial.
3((-6 + -1r)(9 + -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 '(9 + -1r)' equal to zero and attempt to solve:

Simplifying
9 + -1r = 0

Solving
9 + -1r = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1r = 0 + -9
-1r = 0 + -9

Combine like terms: 0 + -9 = -9
-1r = -9

Divide each side by '-1'.
r = 9

Simplifying
r = 9
Solution
r = {-6, 9}