6r^2-15r=-9

Solution for 6r^2-15r=-9 equation:

Simplifying
6r2 + -15r = -9

Reorder the terms:
-15r + 6r2 = -9

Solving
-15r + 6r2 = -9

Solving for variable 'r'.

Reorder the terms:
9 + -15r + 6r2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -15r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -5r + 2r2) = 0

Factor a trinomial.
3((1 + -1r)(3 + -2r)) = 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 '(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
Solution
r = {1, 1.5}