For certain real numbers $a$, $b$, and $c$, the polynomial $g(x)=x^3+a{x}^2+3x+12$ has three distinct roots, and each root of $g(x)$ is also a root of the polynomial $f(x)=x^4+5x^3+b{x}^2+60x+c$. What is $f(-1)$?