Find all ordered pair of integers $(x,y)$ 
Obtain all ordered pair of integers $(x,y)$ such that $$x(x + 1) = y(y + 1)(y + 2)(y + 3)$$

I'm getting 8, 
(0, 0), (0, -1), (0, -2), (0, -3)
(-1, 0), (-1, -1), (-1, -2), (-1, -3)
Please confirm my answer.

HINT Assume $x>0$. Then this question along with the fact that $$x^2 < x^2 + x + 1 < (x+1)^2$$ should do the job. Argue similarly for $x \leq 0$
