Can Mathematica help to rearrange an equation?

That is an extremely general question, but usually, yes.
The commonly used functions used are Solve and Reduce:

Reduce[x^2 + a x + 1 == 0, a]

x != 0 && a == (-1 - x^2)/x

The documentation pages linked above contain many examples. Please read these, and if necessary narrow your question to a specific difficulty or problem.

Since the question was asked, AddSides etc *Sides have been added to Mathematica for the purpose.

Simplify makes some things automatically.