Pat wrote Get a carpet shampooer with rotating brushes. Works great. You use it to spray on some water, let the brushed work, and keep it wet. Then you vacuum up the water. Don't go overboard on the water, though. Beats the heck out of scrubbing by hand.
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Oh no, the secret is out. I have purchased 3 of those devices in garage sales. Never for more than $5. Most come with 3 sets brushes: soft, medium and firm. I have discovered that there is always an appropriate set of brushes for any serious cleaning job.
I've held the base of the unit in my hands and scrubbed walls with it. Vinyl floors and hardwood floors are other good applications. The units work well on automobile carpets and floor mats, used in conjunction with a Hoover style carpet cleaner.
A good power washer works well on most concrete, but a carpet shampooer with the stiffest brushes, used in conjuntion with detergent and bleach, will restore almost any horizontal concrete.
Just don't forget to use a portable GFCI with the shampooer.
Gideon