-6r^2+19r-15=0

Solution for -6r^2+19r-15=0 equation:

Simplifying
-6r2 + 19r + -15 = 0

Reorder the terms:
-15 + 19r + -6r2 = 0

Solving
-15 + 19r + -6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + 3r)(3 + -2r) = 0

Subproblem 1
Set the factor '(-5 + 3r)' equal to zero and attempt to solve:

Simplifying
-5 + 3r = 0

Solving
-5 + 3r = 0

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

Add '5' to each side of the equation.
-5 + 5 + 3r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3r = 0 + 5
3r = 0 + 5

Combine like terms: 0 + 5 = 5
3r = 5

Divide each side by '3'.
r = 1.666666667

Simplifying
r = 1.666666667
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 = {1.666666667, 1.5}