12r^2-3r-54=0

Solution for 12r^2-3r-54=0 equation:

Simplifying
12r2 + -3r + -54 = 0

Reorder the terms:
-54 + -3r + 12r2 = 0

Solving
-54 + -3r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -1r + 4r2) = 0

Factor a trinomial.
3((-2 + -1r)(9 + -4r)) = 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 '(9 + -4r)' equal to zero and attempt to solve:

Simplifying
9 + -4r = 0

Solving
9 + -4r = 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 + -4r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4r = 0 + -9
-4r = 0 + -9

Combine like terms: 0 + -9 = -9
-4r = -9

Divide each side by '-4'.
r = 2.25

Simplifying
r = 2.25
Solution
r = {-2, 2.25}