Dam, Tomato stains?
Gesh does it get any harder then this?
Folex is a great carpet cleaner.
I mainly use Meg's APC+. but you can use just about any APC you have.
You will need a wet vac too.
Spray, brush, vac wipe.
Red satins are the worst. If you have a Janitorial Supply House nearby check with them for some specialty products for removing red stains.