In the above graph it looks to the eye as if the function y is equal to 0 somewhere around x = -3, x = 1, and x = 3. How to find where y=0 is an important question that we will pursue from several directions this semester. But in this case, the question is easily answered because Mathematica is good at factoring polynomials. To see this, execute the following command.
Factor[y]
It is now clear that y = 0 precisely at x=-3, x=1, and x=3.