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.
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.