Question

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:

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