Like you I bought a house last year. The lawn looked terrible but I fixed it right up.
Do this in sections, not the entire yard at once unless you have no job and a lot of time to waste.
1. Set mower deck height to lowest setting and SCALP the section you want to fix.
2. RAKE all the thatch, leaves, grass, and garbage out of the area you scalped.
3. Till the soil up with a garden weasel.
4. Use a drop spreader and put down GOOD PREMIUM seed.
6. Use garden weasel to mix and mash the seed into the soil. The seed must be in CONTACT with DIRT to germinate and start growing. Any seed laying on the ground is wasted.
7. Water AT LEAST twice daily. I did watering in the morning before going to work and again when I got home and once more before bed.
8. 10-14 days later you have grass. Don't mow it until it's 5 inches high. Now set mower deck to second highest setting and leave it there. Always mow your grass on a high deck height setting, short settings are hard on the grass once the summer heat and drought arrive.
9. Pretty grass!
The pic shows an area I repaired myself. Before I started there was NO GRASS there because the previous owner parked his trailer over the grass when he moved out. Over several days the summer heat and lack of sun and killed it all.
Your results may vary.
Good luck.
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