#1
I recently purchased a used ESP EC-401 that is equipped with Grover tuners and it's having difficulty staying in tune. The low 3 strings are usually fine, but the high 3 go out of tune from a simple bend.

I recently changed the strings on it to Ernie Ball Cobalts.

I really don't know what to do.
#2
Sounds like the nut, not the tuners.

Grover makes very nice tuners and they very rarely move once tuned.

Try some Big bends nut sauce or take a #2 pencil and rub it on the nut slots. the graphite from the pencil will hopefully lube the strings so they don't bind.

Having a tech widen the string slots is the best answer
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#4
I'm hardly a tech but those nut slots look too tight for the top three strings. What gauge are they?
#6
Well, since the guitar comes with 10-46 gauge strings (or even 9-42) the slots are cut for those. There is probably nothing wrong with the tuners at all, it's just the strings getting caught in the nut.
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#7
nut slots need to be bigger-- unless you know what you're doing, take it to a reputable shop and have someone take care of it.