6r^2-11r+5=0

Solution for 6r^2-11r+5=0 equation:

Simplifying
6r2 + -11r + 5 = 0

Reorder the terms:
5 + -11r + 6r2 = 0

Solving
5 + -11r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + -6r)(1 + -1r) = 0

Subproblem 1
Set the factor '(5 + -6r)' equal to zero and attempt to solve:

Simplifying
5 + -6r = 0

Solving
5 + -6r = 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 + -6r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6r = 0 + -5
-6r = 0 + -5

Combine like terms: 0 + -5 = -5
-6r = -5

Divide each side by '-6'.
r = 0.8333333333

Simplifying
r = 0.8333333333
Subproblem 2
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
Solution
r = {0.8333333333, 1}