Glass hammer

The easiest solution to find is N=0, by moving all the terms to one side and factoring an N out. Now we do not need to find the other solutions because 0 times anything is $\huge 0$ .

$N = 0$ is a solution. Hence the product must be 0.

There are three solutions of the equation $N^{2}$ + $N$ = $N ^ {3}$ - $N$ namely $(2,-1,0)$ and $2\times(-1)\times(0)=0$

There are three solutions to the above equation: 2, -1, and 0. Therefore, their product is $2*0*-1$ , which is equal to $\boxed{0}$ .