12r^2+34r-6=0

Solution for 12r^2+34r-6=0 equation:

Simplifying
12r2 + 34r + -6 = 0

Reorder the terms:
-6 + 34r + 12r2 = 0

Solving
-6 + 34r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 17r + 6r2) = 0

Factor a trinomial.
2((-3 + -1r)(1 + -6r)) = 0

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

Simplifying
1 + -6r = 0

Solving
1 + -6r = 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 + -6r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6r = 0 + -1
-6r = 0 + -1

Combine like terms: 0 + -1 = -1
-6r = -1

Divide each side by '-6'.
r = 0.1666666667

Simplifying
r = 0.1666666667
Solution
r = {-3, 0.1666666667}