Blow the cement surface off with an electric or gas powered leaf blower and use a shop vac to extract all dirt from the corners and edges along the floor.
Use a putty knife to scrape up any stuck tar, paint or glue spots on the cement flooring.
Add several drops of liquid detergent to a bucket of warm water and use a push broom to scrub the cement surface thoroughly. Rinse with a hose.
Connect a pressure washer to the hose and pressure wash the cement floor. Rinse it out as you wash.
Add half the amount of acid than what is usually called for. For example, instead of using a pound of sulfamic acid powder, which is commonly mixed with one gallon of water to clean 300 square feet of cement, use only a half pound.
Scrub the sulfuric acid wash into the cement evenly and then rinse it well with a hose.