6r^2-7r+1=0

Solution for 6r^2-7r+1=0 equation:

Simplifying
6r2 + -7r + 1 = 0

Reorder the terms:
1 + -7r + 6r2 = 0

Solving
1 + -7r + 6r2 = 0

Solving for variable 'r'.

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

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

Simplifying
1 + -6r = 0

Solving
1 + -6r = 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 + -6r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6r = 0 + -1
-6r = 0 + -1

Combine like terms: 0 + -1 = -1
-6r = -1

Divide each side by '-6'.
r = 0.1666666667

Simplifying
r = 0.1666666667
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 = {0.1666666667, 1}