Determine all ordered pairs $(x, y)$ of nonnegative integers that satisfy the equation $$3x^2 + 2 \cdot 9^y = x(4^{y+1}-1).$$
Source: Philippines MO 2018/4
Tags: number theory, Diophantine equation
Determine all ordered pairs $(x, y)$ of nonnegative integers that satisfy the equation $$3x^2 + 2 \cdot 9^y = x(4^{y+1}-1).$$