I have two bathrooms in my home. When the first floor bathtub drains, the water goes in to the toilet in the basement downstairs and in the shower drain , also in the basement/ bathroom. There is black gunk coming from the floor drain behind the washer and the water goes down very slowly. I have used drain cleaner/drain buildup remover for the last three days and it has not gotten any better. I poured a gallon of bleach in the floor drain behind the washer and still there is black gunk coming up from the drain. Two years ago, I had the same problem and it cost me 300 dollars to get the problem fixed. Is there a cheaper way to do this and what would you recommend?

You have a partial blockage downstream from the basement floor drain that must be snaked.
I have used drain cleaner/drain buildup remover for the last three days and it has not gotten any better. I poured a gallon of bleach in the floor drain I am no fan of putting chemicals in your drainage system. Besides they only seem to work in TV ads.
What do you want to do? Call in a plumber or rent a snake and do it yourself? Let me know, Tom