6r^2-9=-3r

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

Simplifying
6r2 + -9 = -3r

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

Solving
-9 + 6r2 = -3r

Solving for variable 'r'.

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

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

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

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

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

Simplifying
-3 + -2r = 0

Solving
-3 + -2r = 0

Move all terms containing r to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -2r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2r = 0 + 3
-2r = 0 + 3

Combine like terms: 0 + 3 = 3
-2r = 3

Divide each side by '-2'.
r = -1.5

Simplifying
r = -1.5
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 = {-1.5, 1}