Consider $-35x^{2}-16xy+12y^{2}$ as a polynomial over variable $x$.
$$-35x^{2}-16yx+12y^{2}$$
Find one factor of the form $kx^{m}+n$, where $kx^{m}$ divides the monomial with the highest power $-35x^{2}$ and $n$ divides the constant factor $12y^{2}$. One such factor is $5x-2y$. Factor the polynomial by dividing it by this factor.