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

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

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

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

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

Multiply (-2 + 3k) * (-1 + 2k)
2(-2(-1 + 2k) + 3k * (-1 + 2k)) = 0
2((-1 * -2 + 2k * -2) + 3k * (-1 + 2k)) = 0
2((2 + -4k) + 3k * (-1 + 2k)) = 0
2(2 + -4k + (-1 * 3k + 2k * 3k)) = 0
2(2 + -4k + (-3k + 6k2)) = 0

Combine like terms: -4k + -3k = -7k
2(2 + -7k + 6k2) = 0
(2 * 2 + -7k * 2 + 6k2 * 2) = 0
(4 + -14k + 12k2) = 0

Solving
4 + -14k + 12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -7k + 6k2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -3k)' equal to zero and attempt to solve:

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3k = 0 + -2
-3k = 0 + -2

Combine like terms: 0 + -2 = -2
-3k = -2

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Solution
k = {0.5, 0.6666666667}