Dissolve ½ cup of trisodium phosphate in a bucket of hot water. Thoroughly scrub the concrete floor with the mixture, using your scrub brush. Let the floor dry for 48 hours.
Lay a 2-inch by 4-inch board on its narrow edge. Scoot it over the floor slowly, looking for spacing under it to indicate where the floor dips. Mark those areas with a pencil.
Combine powdered floor-leveling compound and water in a bucket in the ratio specified on the packaging of the compound. Mix it well with a wooden spoon. The compound should end up with a very thin, liquid consistency.
Pour the mixed compound over the low spots as marked on the concrete, as well as into any cracks or holes, starting at the far corner of the room from the entrance so you can work your way out of the room. For the low spots, let the compound spread out and find its own level, evening out the surface. Do the whole floor.
Let the compound set for 24 hours. The concrete is now ready for new flooring.