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It appears that you have enough trade lines open. You need more time to get those scores higher. Just pay on time and take another look at your scores in 6 months.
I'm sure you can. My DH still has 5 colections reporting for him (all paid) and we've gotten his EQ from 625 to 656 and TU 616 to 661 since April of this year and alot of it was from getting utilization down. Just keep the lates away!
After about a year your negative doesnt hurt as bad. Just keep things looking good and your util low and your score will grow.
A year ago I was in the 400s, now in the 700s with my EQ score.
I am in the same boat, i am actually buying a home right now... i have like 5-7 collections on my reports... and look at my scores below... i havent been on this journey that long and look where i am at.... you are WELL on your way to being able to purchase!!!