Ok, here's a nice quick guitar tip that will help you keep your guitar in tune. When changing strings on a guitar that has no locking pieces at the nut, right before I put the string into the grove at the top of the neck - I sprinkle some graphite from a pencil. I take the pencil, move it up and down the groove in the nut and enough of the graphite will quickly fall in. I get the big pencils that are used for construction at Home Depot. Then, I put the string in.
Why does it work? Graphite is very slippery and slick and having some of it in the nut helps the string move or adjust as you bend or tune your guitar. If the above doesn't make sense, keep re-reading it until it does. I have been using this trick for years and have found it very helpful.