Answer: First off I would suggest you work with your county extension to run some basic soil tests and see if the soil is suitable for lawn grass. If not, based on the test results, they can tell you how to improve the soil so that grass will grow there. They can also recommend specific grass varieties for your local area that grow better in part shade.
Keep in mind that grass is really a sunlover. Too much shade makes it impossible to grow healthy lawn. So if the area receives less than all morning direct sun, you may need to think about using a groundcover instead. Either way, you will probably need to loosen the soil, add organic matter such as compost, possibly add lime to adjust the pH and then finally plant seed or sod. I hope this helps.
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