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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 \( x = \{0, 6\} \)**.