Dirty water is backing up in the tub and the toilet when the washer is spinning the water out. Now I can't wash or the bathroom will be flooded.

You have a partial clog downstream from the tub and toilet. The solution is to snake the drain line. This can be done from one of two places. You can pull the toilet or you may snake from the lavatory roof vent.
Put out enough snake to reach the base and 15 more fet. Good luck, Tom

There is at least one more option for snaking, if there is access to the drain pipe in question from outdoors. Often, you can use an outdoor cleanout, or the septic tank inlet, as the snake entry point. I like this approach because it leaves the mess outdoors, and sometimes you can see what the blockage was as it floats by. It does require an experienced drain cleaner, who can monitor the snakes location by length of playout, fit, & feel...

I disagree with Mikes . Advice and here is why. You do not snake against the flow . The snake could come up into a fixture and damage it. The correct way to snake any blockage is to snake with the flow of the liquid. Regards, Tom

Sorry,Tom but I have to agree with Mike. There is a reason they make double cleanouts. The most important part of Mikes statement is in the last sentence.

Snaking from outdoors is not always possible, & as I have pointed out, should only be performed by someone with experience, and the ability to keep track of the cables location. Opening an out door cleanout, or digging to expose the inlet baffle of a septic tank is easy and can be effective - I have cleared scores of blocked main drains, simply by removing a blockage from the inlet baffle of a septic tank.
I'm very pleased to participate in this forum. Sharing tips, techniques, experiences, policies, procedures, & opinions, generates valuable discussion that results in the opportunity for learning...

Sorry MikeI'm an old time plumber and snaking against the flow has always been a no no to me. Snaking into a house and coming up under a toilets with a metal tip is it my idea of a job well done. I respect your advice and my girls dad statement . But I still hold that snake against the flow is not good plumbing practice. I have removed the reddie and I apologize for putting it up. Sometimes it's hard to teach an old dog new tricks. Regards, Tom