My kitchen sink keeps backing up into the other side of my double sink. It does it when I use the dishwasher and even when I do not. I have taken a 25 foot snake down the pipes in the sink and I have tried to go through the dishwasher tube as well and I am not finding how to repair the problem. Any suggestions

I'm not sure if this will be much help, since you have snaked your pipes already. But I lived in a house where this happened to me. I was told to pour a couple of cups of baking soda down the drain, followed by a bottle of vinegar, let it sit (it foams up) for a few minutes, and then flush it with boiling water several times. It seemed to work for me at the time. (This method works if you have a smelly sink drain too). Otherwise it may be the way your dishwasher is hooked up. Just thought I would mention this, "just in case". Best of luck to you.