I have a double sink in my kitchen. One of them has a garbage disposal attached. It has been connected for at least 10 years. Now I am having trouble on the side with the garbage disposal. It drains very slowly and when I turn on the garbage disposal, it backs up into the other sink. I have cleaned out the drains and even cleaned out the main drain, but it still is draining slowly and backing up. I have tried using special cleaners for garbage disposals as well. Any suggestions?

Well... hate to say it... but both sinks are probably still clogged in some manner! My favorite (and easiest) attempt to unclog double sinks (even with garbage disposals) is to stuff a rag (or hold stopper) in disposal side and then using a plunger... plunge the sink... The pull is more important than the push (use the push to set the plunger square and attain suction... THEN pull back and up (and I like to have someone else hold down disposal stopper or rag so I can really pull up on plunger!. ALSO NOTE... THIS CAN BE A BIT MESSY!! ).

If this doesn't improve things then I figure you have to snake the drain again. Here, 50% of your snaking attempts may in fact go up the vent instead of down the drain... further, any kind of real clog requires you to really work the snake back and forth in the drain line... especially if pipe turns into cast iron before going underground.

Let us know what kind of pipe... distance... anything else that you think may help... IF ABOVE DOES NOT WORK!!
'
If my answer helped... RATE THIS ANSWER below... thank you.

OK we can tell your problem is after the two sinks come together. When you turn your disposal on you sort of super charge your drain so fill the disposal side with hot water and plug the other drain with a good seal like the strainer that came with the unit and a heavy towel, turn on the disposal. Do this a few times and if you don't see any improvement the plug could be after the vent pipe and like MASS says 50% of the snaking goes up the vent but try it anyway. Check in you basement for any clean outs on this drain line, you should see one.