Introduction
Most of the Mathematics of Engineering/Science consists of relationships between various physical quantities. These are expressed as Mathematical equations.

Examples
1. Area of a circle, radius r
2. Coulombs Law. The force of attraction between two charged particles is
3. Rate of heat transfer Q through a slab of heat conducting material, thickness l is
Equations such as the above which represent frequently used results are known as formulae. When using a formula connecting physical quantitites it is of course important to use a consistent set of physical units, but in this post we are solely interested in the Mathematical rules for manipulating equations.

The Only Rule
There is only one rule for changing the appearance of an equation.
Whatever you do to one side of the equation you must do the same to the other side.