Problem

The curve $C$ has equation

$$2x-4y^2+3x^2y=4x^2+8$$

The point $P(3,2)$ lies on $C$.

Find the equation of the normal to $C$ at the point $P$, writing your answer in the form $ax+by+c=0$ where $a$, $b$ and $c$ are integers to be found.