2021 AMC 12D Question 14

Suppose that $P(z),$ $Q(z),$ and $R(z)$ are polynomials with real coefficients, having degrees $2,$ $3,$ and $6,$ respectively, and constant terms $1,$ $2,$ and $3,$ respectively. Let $N$ be the number of distinct complex numbers $z$ that satisfy the equation $$
P(z) \cdot Q(z) = R(z).
$$ What is the minimum possible value of $N?$