The problem is to solve the quadratic equation $-2x^2 + 6x = 0$.

1. Problem Description

The problem is to solve the quadratic equation $-2x^2 + 6x = 0$.

2. Solution Steps

To solve the equation $-2x^2 + 6x = 0$, we can factor out the common factor, which is $-2x$.

$-2x(x - 3) = 0$

Now, we set each factor equal to zero.

$-2x = 0$ or $x - 3 = 0$

Solving for $x$ in the first equation:

$x = \frac{0}{-2}$

$x = 0$

Solving for $x$ in the second equation:

$x = 3$

3. Final Answer

The solutions to the equation $-2x^2 + 6x = 0$ are $x = 0$ and $x = 3$.