-3r^2+9r-6=0

Solution for -3r^2+9r-6=0 equation:

Simplifying
-3r2 + 9r + -6 = 0

Reorder the terms:
-6 + 9r + -3r2 = 0

Solving
-6 + 9r + -3r2 = 0

Solving for variable 'r'.

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

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

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

Simplifying
-2 + r = 0

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

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

Combine like terms: 0 + 2 = 2
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}