What I didn't expect was 10 to 15 hz. wide nulls (-10,-15,even -20 db.) at several other frequencies.
No need to panic. This is quite normal. Do as Plato suggests first (try speaker positioning).
You will need very serious room treatments for these null problem areas if they are below 60 HZ (and I doubt you can cure them entirely without turning your room into something like a set from Flash Gordon). Fortunately you don't need to cure it entirely. For starters, you can easily reduce the worst bumps with a PEQ. (Bumps are more of a problem due to their masking effect). Although nulls cannot be boosted (can't boost what is not there)....smoothing out the peaks will really help.
Try listening to Rebecca Pidgeon The Raven, "Spanish Harlem" and adjust so that you can hear the bass notes evenly and with roughly equal loudness. Good luck...