Answer
$x=0$; $x=2$;
Work Step by Step
We use a graphing calculator to graph the function $y=-x^4+4x^3-4x^2$.
From the graph we notice that the $x$-intercepts are:
$$\begin{align*}
x_1&=0\\
x_2&=2.
\end{align*}$$
We check if the values $x_1$ and $x_2$ check the equation $-x^4+4x^3-4x^2=0$:
$$\begin{align*}
x_1&=0\\
-0^4+4(0^3)-4(0^2)&\stackrel{?}{=}0\\
-0+0-0&\stackrel{?}{=}0\\
0&=0\checkmark\\\\
x_2&=2\\
-2^4+4(2^3)-4(2^2)&\stackrel{?}{=}0\\
-16+32-16&\stackrel{?}{=}0\\
0&=0\checkmark
\end{align*}$$
Therefore the solutions of the equation are $0$ and $2$.
