jmc

Since we know what $g(2x+5)$ is, to determine $g(-3)$, we must determine what value of $x$ makes $2x+5$ equal to $-3$. Solving $2x+5=-3$ gives us $x=-4$. Letting $x=-4$ in $g(2x+5)=4x^2-3x+2$ gives $g(-3)=4(-4{)}^2-3(-4)+2=4\cdot 16+12+2=\boxed{78}$.