Solve the factored quadratic equation 0 = -1/3x (x - 6).

To solve the factored quadratic equation \( 0 = -\frac{1}{3}x (x - 6) \), we can set each factor to zero.

1. Set the first factor to zero:
\[
-\frac{1}{3}x = 0
\]
This simplifies to:
\[
x = 0
\]

2. Set the second factor to zero:
\[
x - 6 = 0
\]
This simplifies to:
\[
x = 6
\]

Thus, the solutions for the equation are \( x = 0 \) and \( x = 6 \).

The solution set is \( x = \{0, 6\} \).

Therefore, the correct answer is:
**The solution set is \( x = \{0, 6\} \)**.