6r^2=9+15r

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

Simplifying
6r2 = 9 + 15r

Solving
6r2 = 9 + 15r

Solving for variable 'r'.

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

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

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

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

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

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

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

Simplifying
-1 + -2r = 0

Solving
-1 + -2r = 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 + -2r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2r = 0 + 1
-2r = 0 + 1

Combine like terms: 0 + 1 = 1
-2r = 1

Divide each side by '-2'.
r = -0.5

Simplifying
r = -0.5
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-0.5, 3}