Equation with factorials

by Alesak
Tags: equation, factorials
 P: 134 hello everyone, I usually post my questions on one small czech mathematical forum, but here is an equation noone knows how to "solve". Ive came to it by accident, when I made an mistake in one combinatorics equation. $$x! + (x-3)! = 16x - 24$$ its fairly simple to solve in one way(x has to be greater than 2, and from some point left side is greater than right side, because (x-3)! is always greater then 0 and we dont have to care about -24 on the right side, so we can check for which x is x! > 16x. this leaves us only very few possibilities for x to check). this is nice, but Id like to know if its possible to get it in form x = something. I cant think of any way how to do it. also, this equation doesn`t have any solution, its rather theoretical question.