solve the factored quadratic equation 0 = -1/3x (x - 6).

Answer 1

To solve the factored quadratic equation \( 0 = -\frac{1}{3}x (x - 6) \), we can set each factor equal to zero:

1. Set the first factor to zero:

   \[ -\frac{1}{3}x = 0 \]

   Multiplying both sides by \(-3\) gives:

   \[ x = 0 \]

2. 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:

\[ x = 0 \quad \text{and} \quad x = 6. \]