I am stuck trying to figure out a way using C++ to solve a situation where the user inputs a value using cin and then have the computer solve for a way to get the value of cin,
It looks like you have a 'mathematical' problem here: a couple of values constrained by equations, and you want 'the computer' to find all possible values that fit into the constraints (equations). Am I right?
While some computer programs can certainly do that, the C++ language is not designed for this purpose. The role of the C++ is to give you a way of giving instructions to the processor, like "store this value in memory" or "add these two numbers". But there is no way of saying "solve this mathematical problem".
What you need is some equation solver. But I am not familiar with any. There are tools like Matlab or Mathematica. But I do not think they are free.