Solving Equations system question We get  this   equation and need to solve 
Solve in $\mathbb{Z} $ the given equation 
$ y(y -x )(x+1) = 12\ $

If you factor 12 as 3 x 2 x 2 and then put y = 3, y - x = 2, x + 1 = 1, you get a solution x = 1 and y = 3 which is an integer solution. This is by using common sense. The other one can be obtained by writing 12 as -2 x -3 x 2 in which case x = 1 and y = -2 is the other solution. 
