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.

The equation can be rewritten as:

\[ -\frac{1}{3}x(x - 6) = 0 \]

Since the product is zero, we can use the property that if a product is zero, at least one of the factors must be zero.

1. Set the first factor to zero: \[ -\frac{1}{3}x = 0 \] Solving for \( x \): \[ x = 0 \]

2. Set the second factor to zero: \[ x - 6 = 0 \] Solving for \( x \): \[ x = 6 \]

Thus, the solutions to the equation \( 0 = -\frac{1}{3}x(x - 6) \) are:

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