Determine all zeros of the polynomial $X^4 - 2X^3 - X^2 + 2X + 1 \in \mathbb C[X]$. This is Exercise 14 on page 110 of Analysis I by Amann and Escher.
The hint given is as follows: multiply the polynomial by $1/X^2$ and substitute $Y = X - 1/X$.
If I attempt this, I get the following:
\begin{align*}
X^4 - 2X^3 - X^2 + 2X + 1 &= 0\\
\Rightarrow X^2 - 2X - 1 + \frac{2}{X} + \frac{1}{X^2} &= 0.
\end{align*}
My problem is that I don't understand how to make the suggested substitution. I'm wondering if there is something obvious I'm missing.
I appreciate any help.

$Y^2= X^2-2+\dfrac{1}{X^2}$. So $X^2-1+\dfrac{1}{X^2} = Y^2+1$. Then
$$X^2-2X-1+\dfrac{2}{X}+1/{X^2} = Y^2+1-\left(2X-\dfrac{2}{X}\right)=Y^2-2Y+1$$
