This is my favorite trick for a burned pan.

Dishwasher detergent

Put in the bottom of the pan and let set. Sometimes will be clean in
just a few minutes. If it is really bad, you might need to repeat a
couple of times. I bought a really badly burned pan at a garage sale
about twnety years ago, for a quarter. Brought it home and used the
above mixture and I am still using the pan today. You might be
careful with using this on alluminum, but is great for stainless