Backyard

I believe that is crabgrass but it looks a little too frilly.

That's way too much shade for bermuda.

Where do you live?
Why do you want fescue?

I live in Northeast Atlanta, GA. That picture was taken in at 9:30am looking due east. Where the grass is actually growing, it gets a good 7 hours of sun. The area with mostly dirt gets none as it is blocked by the house. I don't necessarily want fescue in the shady part, i just want something that will grow.

It is Crabgrass... "Celsius" will kill most (if not all) of those weeds in the Bermuda. If you are okay with killing the fescue, you can spray it too. Otherwise, do not treat the fescue :) You can pick that up at John Deere Landscapes for ~$80. You will get 40-45 treatments out of that bottle. (more than enough)

With the shade... I see sunlight on a bare area in the photo!

It looks to me like a soil compaction and drainage issue. Maybe, there is a lot of foot traffic along the beds? Maybe with all of the rain we've gotten here in the ATL its just tamping everything even more. Plus, Ga. clay doesn't drain well as it is.

I think you can grow Bermuda there. It's just going to take work. Or you can kill the Bermuda and lay fescue in the back. Either way... Aerate!!! And do it now.

Is that back dead part a walking pathway? If so you might want to do something else with it. I'm thinking of a stone pathway (not pea gravel), pavers, stepping stones, wooden decking path, mulch path...anything but grass.

If people or animals walk there and you still want to keep it in grass, it is going to be a problem. I would not aerate there. I would use shampoo. Search this forum for more information on the use of shampoo instead of aerating.

Yes, Drainage was a big problem before... There was a "ditch" of sorts that kept water away from the house and with any measurable rainfall, the ditch would flood. I decided to install a drainage system with 3 drains along the ditch, tying in 2 gutters spouts. I filled in most of the ditch to even out the yard and drainage is much better.

There is slight traffic in that area just off the patio but not along the pavers.

Here are a couple of pictures of the drain. You can see in the one picture the sunlight problem close to the house. Moss seems to be the only thing that will grow there.

Drain

I also have a small patch of what i believe to be zoysia? Would it make sense to pull plugs from it and plant them along the side of the house?

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Plugging is a good way to plant zoysia. Is there shade next to the house (there almost always is) and does the zoysia like the shade (it almost never does)? There are a couple of zoysia's that do very well in shade, but if you have it in full sun, you probably have the full sun varieties.