Question

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

Answer 1

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:

1. \(x = 0\)
2. \(x - 6 = 0\)

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 \(x = 6\).