The classical result of L. Székelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known that Székelyhidi’s result may be generalized to equations where some occurrences of the unknown functions are multiplied by a linear combination of the variables. In this paper we study the equations where two such combinations appear. The simplest nontrivial example of such a case is given by the equation

considered by Fechner and Gselmann (Publ Math Debrecen 80(1–2):143–154, 2012). In the present paper we prove several results concerning the systematic approach to the generalizations of this equation.

L.Székelyhidi的经典结果指出（在某些假设下）一般线性方程的每个解都必须是多项式函数。众所周知，塞克利希迪的结果可以推广到方程，其中一些未知函数的出现与变量的线性组合相乘。在本文中，我们研究了出现两个这样的组合的方程。这种情况的最简单的非平凡的例子由等式给出

由Fechner和Gselmann考虑（公共数学德布勒森80（1-2）：143-154，2012年）。在本文中，我们证明了有关该方程推广的系统方法的一些结果。