We can solve simple equations in this way:

• If only the desired variable is on the left, succeed: return the input equation.

  
  (= Y (+ (* M X) B)) 
  

• If only the desired variable is on the right, succeed: return the input equation with the arguments reversed.

  
  (= (+ (* M X) B) Y) 
  

• If only an undesired variable is on the right, fail: return NIL.

  
  (= (+ (* M X) B) FOOBAR) 
  

• Otherwise, try using an algebraic law to eliminate the top operator on the right; usually, there are two possibilities to try. Then try to solve the resulting equation; if either one succeeds, return that answer.

The strategy here is to search through every possible legal rewriting of the equation until we get the one we want.

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