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 equal to zero: \[ -\frac{1}{3}x = 0 \] Multiplying both sides by -3 to eliminate the fraction gives us: \[ x = 0 \]
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Set the second factor equal to zero: \[ x - 6 = 0 \] Adding 6 to both sides gives us: \[ x = 6 \]
Thus, the solutions to the equation \(0 = -\frac{1}{3}x(x - 6)\) are: \[ x = 0 \quad \text{and} \quad x = 6 \]