How to isolate a variable in any equation

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The HP 50g graphing calculator has the ISOL function, that takes an equation and a variable, then proceeds to isolate the given variable on this function and return it.

I have a requirement for developing a solution that does exactly that. Does anyone know this algorithm, or can point me to the right direction on where to find this sort of solution?

As it stands I don't even know the math area that deals with that sort of problem.

This Wolfram|Alpha widget does exactly that: http://www.wolframalpha.com/widgets/view.jsp?id=4acbedbe977480d19b7b682d4878cae2

Any help is greatly appreciated.

Example:

Isolating a variable using Wolfram|Alpha