I have an old Rainbow brand dry/wet vacuum that my mom got at a yard sale, similar to this model. My family grew up with this kind of vacuum at home, and it was useful not only for typical carpet sweeping, but also for cleaning up wet messes.
This type of vacuum has a water-filled basin in the bottom to catch whatever gets sucked up.
My question is, can I use a cleaning solution plus this vacuum to shampoo my carpets similar to a Rug Doctor?
EDIT: More information: I'm hoping to clean our apartment's carpet of the dirt build-up from in front of where our couch was before we re-arranged the living room. There is a noticeably darker strip where our feet would sit. I don't think there are any tough stains that need extreme heat to break up, just dirt and a few water-soluble spills here and there.
Our apartment is tiny and only has three carpeted rooms, and only the living room gets regular shoe traffic, so it's the only room I'm thinking of doing this in.