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The invasion of moss in your lawn occurs when you try to grow grass in places that are too shady, too wet, or on very poor soil-conditions that do not support grass. To eliminate moss and prepare the soil for grass, you'll need to change your lawn's growing conditions.
Spread some lime over the area to get rid of the moss, or a cheaper method if you have a fireplace is to lightly spread some of the ashes over the area. If you wet it down, it sort of makes the gray disappear, but it gets rid of the moss.