Confusion about replacing a variable in a expression of parameters

[safwane]

I have the following problem: I have a diophantine equation of the form: $$f(x,a,b)+c=0\tag{**}$$ that has a solution and by reducing it modulo $$p^n$$ I get a congruence of the form
$$h(x,a,b)+c\equiv 0\pmod {p^n}$$where $$x$$ is the **variable** and $$a,b,c$$ are **parameters** and $$p≥2$$ is a prime and $$n$$ is a positive integer. The above congruence has also solutions.

Let $$g(a,b,c)=a+b-2c$$ be a quantity computed **only** from $$a,b,c$$. In my context I want to see if $$g(a,b,c)$$ has a **specific form**. In the $$a,b,c$$ formula, this form is not clear. However, If I replace $$c$$ from $$(**)$$ I get the desired result. Then my question is about the existence of any obstruction related to this operation: Replacing a variable in an expression of parameters.