jmc

We expand the left side and get $2a{x}^2+(3a+2b)x+3b=20x^2+44x+21$. The coefficients of like terms must be equal, so that means $2a=20$ and $3b=21$. So, we get $a=10$, $b=7$, and $a+b=\boxed{17}$. To check, we should make sure that $3a+2b=44$, which holds since $30+14=44$.