-6r^2+19r-8=0

Solution for -6r^2+19r-8=0 equation:

Simplifying
-6r2 + 19r + -8 = 0

Reorder the terms:
-8 + 19r + -6r2 = 0

Solving
-8 + 19r + -6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-8 + 3r)(1 + -2r) = 0

Subproblem 1
Set the factor '(-8 + 3r)' equal to zero and attempt to solve:

Simplifying
-8 + 3r = 0

Solving
-8 + 3r = 0

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

Add '8' to each side of the equation.
-8 + 8 + 3r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3r = 0 + 8
3r = 0 + 8

Combine like terms: 0 + 8 = 8
3r = 8

Divide each side by '3'.
r = 2.666666667

Simplifying
r = 2.666666667
Subproblem 2
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
Solution
r = {2.666666667, 0.5}