[tex]\begin{cases} x=-5\implies &x+5=0\\ x=3\implies &x-3=0 \end{cases}\qquad \implies \underline{a(x+5)(x-3)~~ = ~~\stackrel{0}{y}} \\\\\\ \stackrel{\textit{we also know that}}{P(0)=-30}\implies \begin{cases} x=0\\ y=-30 \end{cases}\implies a(0+5)(0-3)~~ = ~~-30 \\\\\\ a(5)(-3)=-30\implies -15a=-30\implies a=\cfrac{-30}{-15}\implies \boxed{a=2} \\\\[-0.35em] ~\dotfill\\\\ 2(x+5)(x-3)=y\implies 2(\stackrel{F~O~I~L}{x^2+2x-15})=y\implies \underline{2x^2+4x-30=y}[/tex]
Check the picture below.
