I'm afraid there isn't really any special hints and tips apart from trying out a few values until you get a zero!

For example, you get a zero for . Which means that is a factor.

Use long division, or indeed synthetic division, to divide by , and the result will be a quadratic of the form

Then simply write the function as ... and then use normal quadratic methods to factorise the quadratic and find the other two roots! (or use the quadratic formula).