What equations are needed to predict the rise and setting of the moon from any location?
This is a two part question. First, you need an algorithm to compute where the moon is in its orbit at a particular time and day, and then you need an algorithm to convert these coordinates into rise and set times for a given latitude and longitude. It is moderatly difficult to describe these equations in a site like this. It would be easier for you to go to the library and get a copy of the U.S. Nautical Almanac for 1996 whih, in addition to many tables, gives you the basic equations for the lunar orbit. Sorry I cannot give more help!