6r^2+2r-4=0

Solution for 6r^2+2r-4=0 equation:

Simplifying
6r2 + 2r + -4 = 0

Reorder the terms:
-4 + 2r + 6r2 = 0

Solving
-4 + 2r + 6r2 = 0

Solving for variable 'r'.

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

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

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

Simplifying
-1 + -1r = 0

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

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

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

Divide each side by '-1'.
r = -1

Simplifying
r = -1
Subproblem 2
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
Solution
r = {-1, 0.6666666667}