There's dog and cat hair everywhere! How do I get it out of the carpet?

We have burgundy-colored carpets in our living room and dining room, and three pets who seem to do nothing but shed year-round! No matter how many times a week I vacuum the dog and cat hair never seems to get picked up. It's not just the vacuum I use, either. I've tried three different ones and all had the same results.

When I was younger I remember my grandmother sprinkling some sort of powder on the carpet and it got up all the dog hair. Would something like that work? I've tried baking soda, but all that does is deodorize the carpet. It's driving me mad that no matter how much I clean the pet hair keeps coming back!

What can you suggest that is inexpensive and will work every time?

Thank you!