Find all integers of the form $\frac{(x-1)^2(x+2)}{2x+1}$ I made a python program and I have that
\begin{array}{|c|c|}
\hline x & \frac{(x-1)^2(x+2)}{2x+1} \\\hline
  -14 & 100 \\\hline
-5& 12 \\\hline
-2&0 \\\hline
-1&4 \\\hline
0&2 \\\hline
1&0 \\\hline
4&6 \\\hline
13&80 \\\hline
  \end{array}
And taking very large intervals of integers this seems like the only integers of this form.
However I don't know how can i proved.
Any ideas?

$\bmod 2x\!+\!1\!:\ \, x\equiv -\dfrac{1}2\ $ so $\ 0\equiv(x\!+\!2)(x\!-\!1)^2\equiv\dfrac{3}2 \left[\dfrac{-3}2\right]^2\equiv \dfrac{27}8\iff 27\equiv 0$
