You can slather on conditioner and start picking out mats with a comb. But every time a mat gets wet from bathing it tends to tighten up. Demating should really be done pre bathing.
Products for horses like show sheen can help, but really it depends upon how matted the dog really is. Unless it's your show dog, and I'd hope people showing wouldn't let a coat get like that, often it's not worth the tediousness to demat a dog. Can be kinder to shave it and be more vigilant about brushing in future as the coat grows back in.
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There's a product called Ultra D D-Matting Spray. I've used it & it does help brush mats out after a dog is dry. A slicker brush works best, but even then it can be very time consuming. The easiest way out is, of course, shaving your dog.
Everything depends on the mats themselves. How tight, home many, how close to the skin, etc. How many times have the mats gotten wet? Removing matts no matter what method you chose can be extremly painful depending on the size and tightness of the mats themselves. You can also damage the skin, bruise the dog, etc. If the dog is not used to being brushed, whick I am assuming it is not since it is mated, you could have a real fight on your hands. Not to mention if the dog hurts becuase of it, you may end up with a dog that bites to be brushed.
As a groomer, and a person who has seen all kinds of mats, and most products really are not successful for truly making demating painless. A good shave, and then start from scratch. Don't let the dog get like that again. Almost every client I have had has this problem with the dogs turn around a year old and the coat changes.
Put yourself in your dogs paws. If the hair on your head was a large tight knot, and someone came along and pulled and pulled on it to get it out, how would you feel????
If the mats are that bad, and he is not used to being brushed. I suggest taking him to your vet. Many vets will sedate them to avoid them having pain and shane them down for you. Be sure to follow a strict grooming schedule after that so not to have to go through that again.
Not too many groomers are going to be willing to dematt your dog, especially if you are unwilling to maintain the dog at home (brushing). Dematting is hard work and is time consuming so be prepared to pay. Take the dog to a groomer and see what they recommend. If they suggest shaving, then go with that. If you want to go back to the long coat ask if the groomer will give you some pointers on brushing when the coat starts to come in. Be honest with yourself though, if you aren't commited to brushing then keep your baby in a shorter cut. I adopted my Maltese at 1yr and he was a matted mess. I used an entire bottle of conditioner was able to get most of the mats out, but his hair was so damaged (brittle, stained, broken) that I ended up shaving him anyway. It took about six months, but his coat came in beautifully!