-6r^2+5r=-6

Solution for -6r^2+5r=-6 equation:

Simplifying
-6r2 + 5r = -6

Reorder the terms:
5r + -6r2 = -6

Solving
5r + -6r2 = -6

Solving for variable 'r'.

Reorder the terms:
6 + 5r + -6r2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 5r + -6r2 = 0

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

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 '(2 + 3r)' equal to zero and attempt to solve:

Simplifying
2 + 3r = 0

Solving
2 + 3r = 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 + 3r = 0 + -2

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

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

Divide each side by '3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Solution
r = {1.5, -0.6666666667}