Mormon included two complete letters discussing this situation. When it came to what happened to resolve it, Mormon gave only the briefest of descriptions. That should inform us, as readers, that it was not the military action that was important, but rather the principles that we might discern from the two letters.
The resolution is that Moroni combined with Pahoran, and that gave them a military advantage in numbers, which they used to defeat Pachus, who had been declared king. Mormon took longer than that single sentence, but not much longer.