Let’s balance a more difficult equation today:

Here’s the equations based on conservation of particles:

Carbon (C) | |

Hydrogen (H) | |

Oxygen (O) |

From the carbon and hydrogen equations we get:

From the oxygen equation (with substitutions for c and d based on the carbon and hydrogen equations above) we get:

Now, let’s line them all up together:

We need to eliminate the numerical coefficients in the numerator. We divide everything by 4:

Once we are satisfied that there is no factor common to all 4 of the denominators, we accept the denominators as the solution we are interested in:

Verify it if you’re sceptical!