9r^2-3=-6r

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

Simplifying
9r2 + -3 = -6r

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

Solving
-3 + 9r2 = -6r

Solving for variable 'r'.

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

Combine like terms: -6r + 6r = 0
-3 + 6r + 9r2 = 0

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

Factor a trinomial.
3((-1 + -1r)(1 + -3r)) = 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 + -3r)' equal to zero and attempt to solve:

Simplifying
1 + -3r = 0

Solving
1 + -3r = 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 + -3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3r = 0 + -1
-3r = 0 + -1

Combine like terms: 0 + -1 = -1
-3r = -1

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Solution
r = {-1, 0.3333333333}