I rent a slice seeder in fall, use three blend fescue from jd-lesco. It takes about 21 days to come in. Fine Fescue is good for Northern climates, good disease and pest resistance, drought tolerance, slow growing = less mowing. It likes a 4" cutting height.
Criss -Cross pattern on the slice seeding creates a nice carpet. I time it with a string of rainy days so it comes in nice.
I fertilize twice in the fall with a 19-19-19 6-8 weeks apart.
Putting down the bayer merit in late april to control grubs.
Dont use hay use straw, hay has seeds that you dont want.
You can also buy fiber mulch and soak it with seed in a drum for a few days it will speed up the process then pump it out.
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