3k(3k-2)=0

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

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

Reorder the terms:
3k(-2 + 3k) = 0
(-2 * 3k + 3k * 3k) = 0
(-6k + 9k2) = 0

Solving
-6k + 9k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3k'.
3k(-2 + 3k) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
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, 0.6666666667}