Serran21:
Can you please fully describe the flooring you have and the adhesive that's holding it down to the concrete floor.
Normally, these adhesives are removed with solvents, but there is a bit of a trick to removing them.
Essentially, you need to mop the floor with water so that the concrete absorbs water and becomes damp. Once the concrete (or wood) is damp, it won't absorb any hydrocarbon solvent used to dissolve the adhesive.
The only difficulty is that some old solvent based adhesives aren't very permeable to water and will act as a physical barrier to water. In that case you need to remove the old adhesive at some "starting points" in order to allow the concrete to get wet at those starting points. This can be done with a heat gun and a "Nestor Scraper", (named after it's inventor). A Nestor scraper is made by simply gripping a single edge razor blade in a pair of "needle nose style" locking pliers. The all-metal Nestor scraper will tolerate the heat thrown by the heat gun and can be sharpened quickly and easily by replacing it's inexpensive blade. Simply heat the old adhesive and shave it off the concrete with the Nestor scraper. Wear work gloves on your working hand as the Nestor scraper will get very hot in time.
So, essentially the process to remove a difficult adhesive (like the "black out" used to stick old floor tiles down, would be:
1) Mop the floor with water and cover with plastic so that the water doesn't dry, but permeates through the concrete. Do this repeatedly until you know that all of the concrete under the plastic is damp with water.
2) Now, with the concrete damp, use a solvent to dissolve the old flooring adhesive. The damp concrete won't absorb any of the solvent, so the old flooring adhesive dissolved in that solvent won't leave a stain on the concrete because it's not absorbed into the concrete. Use a steel wire brush to ensure that the old flooring adhesive is fully dissolved into the solvent.
3) Add a detergent to the black solvent mess on the floor. (I'd use Simple Green or Mr. Clean or a 50/50 mixture of the two.) Essentially, the difference between a "soap" and a "detergent" is that soaps are made from naturally occuring materials like plant oils and animal fats. Detergents are made from chemicals. In both cases, the cleaner molecules will have a water loving (or "hydrophillic") group at one end and of the cleaner molecule and a "dirt" group at the other end (that's as chemically similar to the dirt you want to remove as possible. We need cleaner molecules to be made that way so that the dirt end of the cleaner molecule will dissolve in the dirt you want to remove and the hydrophillic end of the cleaner molecule will dissolve in the water you're cleaning the dirt up with.
By adding detergent to the liquid mess of adhesive dissolved in solvent that's on the floor, the "dirt" end of the detergent molecules dissolves in the solvent just like the adhesive.
4) Now we add water and mix it into the solvent mess on the floor with a steel wire brush. When we do that we get an "emulsion" formed. An emulsion is nothing more than one liquid suspended in another. When we add water and scrub, the solvent based mess on the floor breaks into an emulsion of gazillions of solvent droplets with the adhesive dissolved in that solvent, all suspended in the water. The detergent molecules will all be at the surface of those droplets with the hydrophillic ends inside the water and the "dirt" ends inside the solvent.
5. Since the adhesive is now dissolved in the solvent and the solvent is an emulsion on the floor, we can clean that emulsion off the floor with a sponge and bucket of water. Expect the sponge to get dirty as the droplets of solvent will break and release dirty solvent which will soil the sponge. Using a wet/dry vaccuum cleaner to clean the emulsion off the floor would also work well. Dispose of the dirty water you clean up off the floor by pouring it into a storm sewer on your street or avenue to prevent getting your own drain piping dirty with the stuff.