The constant term of the product of two polynomials is just the product of the two constant terms. Therefore we know that $ 6=-2a $, so $ a=-3 $. We now consider the linear term of the product of our polynomials. It's given by $ -16t=(5t\cdot-2)+a\cdot bt\Longrightarrow-16t=-10t+(-3)bt\Longrightarrow b=2 $. Therefore our answer is $ a+b=\boxed{-1} $.