jmc

We will complete the square on the given quadratic expression to find the vertex. Factoring $-3$ from the first two terms, we have $$y=-3(x^2+10x)-81$$In order to make the expression inside the parentheses a perfect square, we need to add and subtract $(10/2{)}^2=25$ inside the parentheses. Doing this, we get $$y=-3(x^2+10x+25-25)-81=-3(x+5{)}^2-6$$The graph of an equation of the form $y=a(x-h{)}^2+k$ is a parabola with vertex at $(h,k)$, so the vertex of our parabola is at $(-5,-6)$. Thus, $n=\boxed{-6}$.