Given:
[tex]x^3-3x^2+2x=0[/tex]To determine the solutions, we find the factors of the given function. So,
[tex]\begin{gathered} x^3-3x^2+2x=0 \\ \text{Simplify} \\ x(x^2-3x+2)=0 \\ \end{gathered}[/tex]Next, we factor x^2-3x+2=0:
[tex]\begin{gathered} x(x^2-3x+2)=0 \\ x(x-2)(x-1)=0 \end{gathered}[/tex]Then,we find the values of x:
x=0
x-2=0
x=2
x-1=0
x=1
Therefore, the solutions are:
x=0, x=1, x=2
