jmc

We know that $(ax+b{)}^2+c=(a^2)x^2+(2ab)x+b^2+c,$ meaning that if this to equal $9x^2-30x-42$, we start with $a^2=9,$ and so we let $a=3.$ Then, $2ab=-30,$ so $b=-5.$ We do not need to find $c$ in this case, so our answer is $ab=\boxed{-15}.$

Note: Letting $a=-3$ gives us $(-3x+5{)}^2+c,$ which gives us the same answer.