Taylor series for $|y|^x(2-y)=1$?

Question

Knowking that $$|y|^x(2-y)=1$$ for $y\neq1$;

How can one discover a series expression for $y$? That is, how can one discover a series expression for the root of the characteristic polynomial of a x-bonacci sequence?

One thing to note is: $$x=-\log_{|y|}(2-y)$$