3r^2-6r=-3

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

Simplifying
3r2 + -6r = -3

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

Solving
-6r + 3r2 = -3

Solving for variable 'r'.

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

Combine like terms: -3 + 3 = 0
3 + -6r + 3r2 = 0

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

Factor a trinomial.
3((1 + -1r)(1 + -1r)) = 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 + -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 = {1, 1}