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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Start by rewriting the equation: \[ -\frac{1}{3}x(x - 6) = 0 \]
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Since the product is equal to zero, we can set each factor to zero:
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The first factor: \[ -\frac{1}{3}x = 0 \] Multiplying both sides by -3 gives: \[ x = 0 \]
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The second factor: \[ x - 6 = 0 \] Adding 6 to both sides gives: \[ x = 6 \]
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Therefore, the solutions to the equation are: \[ x = 0 \quad \text{and} \quad x = 6 \]
The solutions to the factored quadratic equation are \( x = 0 \) and \( x = 6 \).
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