Combustion is a basic process of burning, where Oxygen is used and the resultants contain Water and Carbon Dioxide. Methane gas burning would work based on this equation:
Incomplete combustion is when the reaction does not fully take place when there is not enough Oxygen to react with:
The products are either raw carbon (C) with water OR carbon monoxide. Incomplete combustion is not wanted because of following reasons:
Usually this process happens when there is enough oxygen to react and results are given off as best as possible.