6r^2+3r-3=

Solution for 6r^2+3r-3= equation:

Simplifying
6r2 + 3r + -3 = 0

Reorder the terms:
-3 + 3r + 6r2 = 0

Solving
-3 + 3r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + r + 2r2) = 0

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

Ignore the factor 3.
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 '(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
Solution
r = {-1, 0.5}