3r^2+3r-6=0

Solution for 3r^2+3r-6=0 equation:

Simplifying
3r2 + 3r + -6 = 0

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

Solving
-6 + 3r + 3r2 = 0

Solving for variable 'r'.

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

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

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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 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 + -1r = 0 + 2

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

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

Divide each side by '-1'.
r = -2

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