That British for what we Americans would call "solve the equation for x".
chuckienz, you solve an equation, or make x the subject of the equation, by "reversing" what has been done to x. Here, the equation is XA+ BA= B.
If I were given a value for A and asked to evaluate the left side, I would do two things: first multiply by A, second add BA. Here, you want to do the opposite. The opposite of "multiply by A" is "divide by A" or, same thing, "mutiply by A-1". The opposite of "add BA" is "subtract BA". Also, you because you are "reversing" everything you must also reverse the order. And, of course, anything you do to the left side of the equation, you must do to the right side.
1) Subtract BA from both sides of the equation.
2) Multiply both sides of the equation by A-1.