(3r^2)-15r+18=0

Solution for (3r^2)-15r+18=0 equation:

Simplifying
(3r2) + -15r + 18 = 0

Reorder the terms:
18 + -15r + (3r2) = 0

Solving
18 + -15r + (3r2) = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -5r + r2) = 0

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

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

Simplifying
2 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
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 = {2, 3}