9r^2-9r-54=0

Solution for 9r^2-9r-54=0 equation:

Simplifying
9r2 + -9r + -54 = 0

Reorder the terms:
-54 + -9r + 9r2 = 0

Solving
-54 + -9r + 9r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-6 + -1r + r2) = 0

Factor a trinomial.
9((-2 + -1r)(3 + -1r)) = 0

Ignore the factor 9.
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 '(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
Solution
r = {-2, 3}