(6k-1)(k-1)=0

Solution for (6k-1)(k-1)=0 equation:

Simplifying
(6k + -1)(k + -1) = 0

Reorder the terms:
(-1 + 6k)(k + -1) = 0

Reorder the terms:
(-1 + 6k)(-1 + k) = 0

Multiply (-1 + 6k) * (-1 + k)
(-1(-1 + k) + 6k * (-1 + k)) = 0
((-1 * -1 + k * -1) + 6k * (-1 + k)) = 0
((1 + -1k) + 6k * (-1 + k)) = 0
(1 + -1k + (-1 * 6k + k * 6k)) = 0
(1 + -1k + (-6k + 6k2)) = 0

Combine like terms: -1k + -6k = -7k
(1 + -7k + 6k2) = 0

Solving
1 + -7k + 6k2 = 0

Solving for variable 'k'.

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

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

Simplifying
1 + -6k = 0

Solving
1 + -6k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6k = 0 + -1

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

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

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

Simplifying
k = 0.1666666667
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1k = 0 + -1
-1k = 0 + -1

Combine like terms: 0 + -1 = -1
-1k = -1

Divide each side by '-1'.
k = 1

Simplifying
k = 1
Solution
k = {0.1666666667, 1}