I just bought a house, and I went to hook up the washer and dryer, and let me add that the utility room is in the basement fully underground. I ran the washer through a trial run and as the water was draining I noticed water coming from under the machine. After further review of the area I noticed that there is a large drain in the floor, about 3" wide going straight down to who knows where, this is where my backup was coming out of. The actul washer drain is a pvc tube coming from the wall like normal, so as the water goes into the normal drain it overflows out the floor. I have tried to snake the drain in the floor, and could not find any other opening, so that did not work. I assume both drains lead to the main septic line going to the street, but I don't know what to try next. The bathroom sink and toilet flush no problem in the bathroom right on the other side of the wall. Please help!

You have three places to snake from. Two places have traps with return bends that you will have to work around. The floor drain and the washer stand pipe. You may also snake from the washer roof vent. One way or another that line has to be snaked and cleared. Good luck, Tom