The practical complication is that (i) the set of possible compounds that may appear as additional reactants or products is too large for brute force enumeration, and (ii) even if this were possible, not all choices that formally might solve the problem are chemically plausible. To simplify the notation further, we can treat the charge as an additional formal "atom type" that may take on both positive and negative integer values, corresponding to positive and negative charges, respectively. This amounts to considering free electrons e -as a special compound. Moreover, we write n - q and n + q instead of q -and q + for the net charge in the following. Note that by convention a free electron e -corresponds to a charge of -1. In the remainder of this section, we describe two alternative strategies for rebalancing chemical reactions.