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Shade is always a problem. Depending on what creates the shade, pine, oak, their drops make the soil more acid. That means you need to add lime. That's a slow acting remedy and may have to be repeated annually. Using moss killers is really a temporary, small area fix. Maybe you can plant something besides grass? Pachysandra does well in shade and tolerates acid soil. Same with Myrtle (Vinca). I like both as ground covers because the fill in well after a couple of years and grow thick enough that leaves don't penetrate. Control the edges with your lawnmower, no trimming needed and no edging needed either. Scotts, probably others, offers a grass seed intended for shade, but high acid will still be a problem that needs to be resolved. Inexpensive soil test kits are available at local garden centers.