You have your work cut out for you. It will be a nasty long drawn out procedure.
Somewhere in the distant past of construction history an evil genius invented a way to glue down flooring on subfloors and sold the idea - use a sticky non hardening paste with all the qualities of chewing gum to keep the covering held down.
I now relegate him to the same compartment in Hell where all the users of red hi temp gasket maker reside. May he agonize forever for his horrible misdeed.
If you have done a remodel and approached this little chore lightheartedly, thinking "How much work can it be?" you know what I am about to recount. A terrorist hijacking a plane to crash it has more honest motives than someone who glues down carpeting with mastic. I can no doubt get hundreds here to agree.
You are, after all, attempting to scrape up a gelatinous paste chosen for it's exact resemblance to the legendary "oobleck" of Dr. Suess' fame. It should go so easy. Mr Incredible got off lightly when hit by the auto firing blob gun.
This noxious substance is often used to glue down carpeting on concrete - yup, commonly used in mall stores - but don't let that be an excuse for you to copy the practice. Said garage floors are often in basements, and as we ALL know, no basement is ever completely free of being underwater. It will happen considering it's below grade, and constitutes a huge bucket that can contain thousands of gallon from any source, around it or above it. Perforate the outer shell and you will be wading on that wonderful carpeting you or the previous owner spent thousands of dollars to install. The money is a complete waste and we know it. It's the innocents who haven't yet flooded their basement who remain blissfully ignorant.
The smell of that carpeting breeding in an oversized petri dish of bacteria and fungus will cure them of their innocence. So, it has to come out, the sooner the better. But, wait - it just doesn't roll up and go out the nearest exit, NOOOOoooooooo, it's glued down by Satan's Snot, and HE is in control of your doom.
First you rip it out by hand in strips you cut with sharp blades, and the frustration of doing that starts to build. It usually leaves the backing stuck to the mastic, which should give pause to your task as the glue is obviously stronger than the cheap bonded junk that was laid over it. You will be left with a spongy wet mass of somewhat interlocking fibers barely capable of being released from a grid of much stronger fibers which now protects and traps the glue.
What fun!
Now you have a sticky layer of adhesive which has bonded to the concrete, and which is demonstrating all the resolve of a three year old in the toy aisle before Christmas clutching at it's prize. Yes it's time for a tool. You can use a razor blade to separate it's grip from the surface - which is highly intense labor. Ok, put down a strong mix of detergent, like a renown dish cleaner which is ironically labeled after the rising sun in the morning. Stir that around working to separate the bond from the substrate and yes, the dawn will emerge - you have just made things exponentially worse. It would be better to have entered a bio haz mat area and snagged your moon suit than be on your feet bent over pushing a long handled blade in a softening gel of massive stickiness. Yes, you will have sucess! Yes, you will step out of your shoes glued to the floor and then your socks!
It is the doom that awaits you, go rent a floor scraper to remove the enormously thick layer that Satan expectorated on your floor and get most of it up first. Once home from the rental shop - and forget about dodging the clean up fee - fire up the scrap, adjust the angle of attack, and watch as thin portions of oobleck are removed leaving a stickier more grippy layer underneath.
You will never wear those shoes in the house again. Choose carefully. Applying water over the top does help but yes, plan on seeing the insole speckled with mastic and future use should be scheduled for the next barn burning you attend. They will be excellent soaked in petroleum and thrown into the hayloft. Hopefully it's at the farm owned by the inventor.
Scrape with all your might, clean small strips of concrete at a time, and watch as the mess grows with every pass actually getting worse as you imagine you are doing better. TIP: if you leave the grid backer down it comes up easier. Cross cut it in 10" squares and have your partner in purgatory remove them as soon as you can. Bag them to prevent allowing this substance from instantly reproducing. It has the ability of subatomic rabbits to replicate exponentially by the microsecond.
Oh, too late, you stepped on a lunger and now Satan has you in his embrace. Buuahahahahahahaaaa! DOOMED! DOOMED!
Just deal with it. Don't go overboard with the dish detergent and scraping, limit it to 4x4 sections or it will get out of control. It will get out of control and you will be lucky to live through it.
Do you want to entertain the idea of being strung up in your basement like Shelob's prey waiting to have your juices sucked from your helpless wriggling body?
The Horror. The HORROR.
This job can be done. Hire others. Pay them the money. Don't be there and accept however it's done with gratefulness. Or - schedule yourself for the worst moment of your remodeling career and accept the flashbacks that will come. You can get this off the floor. You can then proceed with your fantasy vision of a newly redecorated room knowing you are dumping wheelbarrows of cash into a guaranteed loss of home resale value. You can eventually sleep and not dream of sinking into a sea of oobleck with it starting to fill your mouth and nose while you struggle uselessly. It can be done.
You could have a lot more fun rewiring the dashboard of an CJ5, too. Choose that and leave the basement to others. Remodeling a room with glued down carpeting on concrete is a very special station on the seven steps to Hell. If you sink to that depth and survive, then you know that 1) you won't ever do it again, or 2) you now have a very salable skill set and you need to charge accordingly.
Just make sure you have some way to make money on the sale of their first born. That's the profit. Not the work.