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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The first factor: \[ -\frac{1}{3}x = 0 \] To solve for \(x\): \[ x = 0 \]
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The second factor: \[ x - 6 = 0 \] To solve for \(x\): \[ x = 6 \]
Thus, the solutions to the quadratic equation are: \[ x = 0 \quad \text{and} \quad x = 6 \]
Therefore, the solution set is: \[ {0, 6} \]
The correct response is: The solution set is \(x = {0, 6}\).