6r^2-14r-12=0

Solution for 6r^2-14r-12=0 equation:

Simplifying
6r2 + -14r + -12 = 0

Reorder the terms:
-12 + -14r + 6r2 = 0

Solving
-12 + -14r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -7r + 3r2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -3r)' equal to zero and attempt to solve:

Simplifying
-2 + -3r = 0

Solving
-2 + -3r = 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 + -3r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3r = 0 + 2
-3r = 0 + 2

Combine like terms: 0 + 2 = 2
-3r = 2

Divide each side by '-3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
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 = {-0.6666666667, 3}