now, if the roots are -2 and 3, that simply means [tex]\bf \begin{cases}
x=-2\implies &x+2=0\\
x=3\implies &x-3=0
\end{cases}[/tex]
now, as far as the leading term's coefficient having a 3, we can simply make it a "common factor" of both terms.
[tex]\bf \begin{cases}
x=-2\implies &x+2=0\\
x=3\implies &x-3=0
\end{cases}\implies (x+2)(x-3)=0
\\\\\\
\stackrel{\textit{common factor}}{3}(x+2)(x-3)=\textit{original polynomial}
\\\\\\
3(x^2-x-6)=y\implies 3x^2-3x-18=y[/tex]
