All you need to do is factorising all the terms
Now you draw a table and insert all the terms in the first coloumn. In the first line you drop all your zeros. Then you check when a single term is negative, zero or positive and mark it in the table with + and -. For a place where the function does not exist mark an x. The last line of the tabel is for the expression as a whole. Mutliply all + and - from a column and mark the result. So you can find easily where the function has which sign. This works fine for every function. No matter how complex, however it can take quite a lot of time andyou need to find the factorized form.