12r^2-114r-60=0

Solution for 12r^2-114r-60=0 equation:

Simplifying
12r2 + -114r + -60 = 0

Reorder the terms:
-60 + -114r + 12r2 = 0

Solving
-60 + -114r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-10 + -19r + 2r2) = 0

Factor a trinomial.
6((-1 + -2r)(10 + -1r)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -2r)' equal to zero and attempt to solve:

Simplifying
-1 + -2r = 0

Solving
-1 + -2r = 0

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

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

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

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

Divide each side by '-2'.
r = -0.5

Simplifying
r = -0.5
Subproblem 2
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
Solution
r = {-0.5, 10}