To solve the factored quadratic equation \( 0 = -\frac{1}{3}x (x - 6) \), we can set each factor equal to zero:
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Set the first factor to zero:
\[ -\frac{1}{3}x = 0 \]
Multiplying both sides by \(-3\) gives:
\[ x = 0 \]
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Set the second factor to zero:
\[ x - 6 = 0 \]
Adding \(6\) to both sides gives:
\[ x = 6 \]
Thus, the solutions to the equation \( 0 = -\frac{1}{3}x (x - 6) \) are:
\[ x = 0 \quad \text{and} \quad x = 6. \]