Sadly once the scratches are there, no cheap tricks will work. You can however get a window polishing kit which can attach to strong power drill. It takes time since you have to polish the glass slowly in small sections at a time. I did mine and took me about 3 passes with the Cerium oxide, I did it over the course of a week and it eventually worked.
If it's really really bad, you'll have to buy a glass sanding kit too, but I doubt yours will be that bad.
I'd start off with either of these solutions, which will get like 80-100% percent of the scratches out. Afterwards if you see a few hardcore scratches (and you are to OCD) then you'll need to buy a glass sanding kit.