(3k-1)(2k-1)=0

Solution for (3k-1)(2k-1)=0 equation:

Simplifying
(3k + -1)(2k + -1) = 0

Reorder the terms:
(-1 + 3k)(2k + -1) = 0

Reorder the terms:
(-1 + 3k)(-1 + 2k) = 0

Multiply (-1 + 3k) * (-1 + 2k)
(-1(-1 + 2k) + 3k * (-1 + 2k)) = 0
((-1 * -1 + 2k * -1) + 3k * (-1 + 2k)) = 0
((1 + -2k) + 3k * (-1 + 2k)) = 0
(1 + -2k + (-1 * 3k + 2k * 3k)) = 0
(1 + -2k + (-3k + 6k2)) = 0

Combine like terms: -2k + -3k = -5k
(1 + -5k + 6k2) = 0

Solving
1 + -5k + 6k2 = 0

Solving for variable 'k'.

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

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

Simplifying
1 + -3k = 0

Solving
1 + -3k = 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 + -3k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3k = 0 + -1
-3k = 0 + -1

Combine like terms: 0 + -1 = -1
-3k = -1

Divide each side by '-3'.
k = 0.3333333333

Simplifying
k = 0.3333333333
Subproblem 2
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 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 + -2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {0.3333333333, 0.5}