can i suggest a really simple way to do general solutions.
just solve for x-axis intercepts as normal, then add + period x n where n E z to the end of the two adjacent intercepts, and you are done.
Sorry but what do you mean by the end of the two adjacent intercepts? Sorry i'm really tired x_x
just add what I said to two intercepts that are next to each other, otherwise you will end up doing the same solution twice...because remember, if you add on a period to one solution, you will skip the next one, and end up at the one after that, which is just a period further down or up the x-axis. picture a graph if you don't get what i mean.
also, i have realised that this is nearly impossible for them to test, as everyone will have different answers which the examiner would need to waste time checking as they are all theoretically correct.