`-1/2 x^3 + 3/2 x^2 - x = 0`
`⇒ x(-1/2 x^2 + 3/2 x - 1) = 0`
`⇒ -1/2 x^2 + 3/2 x - 1 = 0`
`⇒ -1/2 x^2 + 1/2x + x - 1 = 0`
`⇒ -1/2 x (x - 1) + (x - 1) = 0`
`⇒ (x - 1)(-1/2 x + 1) = 0`
`⇒` \(\left[ \begin{array}{l}x-1=0\\\dfrac{-1}{2} x+1=0\end{array} \right.\) `⇒` \(\left[ \begin{array}{l}x=1\\x=-2\end{array} \right.\)