The balanced decomposition chemical equation for hexane (C₆H₁₄) is:

C₆H₁₄ → 3C₂H₄ + H₂

This equation represents the decomposition of hexane into three molecules of ethylene (C₂H₄) and one molecule of hydrogen gas (H₂).

However, it's important to note:

* This reaction doesn't occur easily under normal conditions. It requires high temperatures and/or a catalyst to initiate the decomposition.

* The products of the reaction can vary. The exact products depend on the conditions used for the decomposition. Other possible products include methane (CH₄), ethane (C₂H₆), propane (C₃H₈), and various unsaturated hydrocarbons.

So, while the above equation is a balanced representation of one possible decomposition, it is not the only possible outcome.