Bad credit score is OK, but poor rental history depends on the reasons they give me. "I was going through a divorce" or "my mom died", things I can verify. I have asked for death certificates and divorce agreements before. If it was "the landlord didn't fix the sink in a timely manner" then they can fuck right off.
Now, I can respect you for that. Those are valids reasons.
Two people have broken leases, I am not sure the reason.