DWV for new basement bath and laundry

[Theory]

Hi Guys,

I just moved into our first house last week and we are re-doing the basement and adding a half bath. I've attached a sketch showing the old and the new.

Due to the laundry/bath config there will be a long run around a wall to the main drain,~15'-20'. I was hoping if I used the right fittings and venting setup this would work: 2" drain shared by the laundry stand pipe and the lav sink.

Do you see any major concerns?

I appreciate the help. I've been trying to wrap my head around venting/draining for the last week trying to figure out the setup. It was very hard to find a spot to accomodate the dryer vent, and plumbing venting which is why I'm not left with many options.

Here is a nice link to Bert Polk's plumbing tips