I’m working on an algorithm where a section of it appears to boil down to a modular arithmetic problem, but unfortunately my modular math sucks. Does anyone here know how to solve modular equations?

Basically this is what I want. As an example, say I’m trying to solve for x in the equation (4x-6)%7=0. Doing a little trial and error, you can find out that x=5+7n where n can be any integer>=zero, so 5, 12, 19 etc are all answers. But when dealing with big numbers, then trial and error obviously can’t be done in my algorithm. So does anyone know how to solve the generic equation (Ax-B)%C=0?