To solve the factored quadratic equation \(0 = -\frac{1}{3} x (x - 6)\), we first identify the factors of the equation. The equation can be set to zero:
\[ -\frac{1}{3} x (x - 6) = 0 \]
For a product to be zero, at least one of the factors must be zero. Since \(-\frac{1}{3}\) is a constant and cannot be zero, we set the other factors to zero:
- \(x = 0\)
- \(x - 6 = 0\)
For the second equation, we solve for \(x\):
\[ x - 6 = 0 \implies x = 6 \]
Thus, the solutions to the equation are:
\[ x = 0 \quad \text{and} \quad x = 6 \]
So, the solutions to the factored quadratic equation \(0 = -\frac{1}{3} x (x - 6)\) are \(x = 0\) and \(x = 6\).
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