According to this example using the Laplace Transform, I am just curious to HOW we go from
$Y(s)=\frac{32}{s*(s^2+12s+32)}$
to
$Y(s)=\frac{32}{s*(s+4)*(s+8)}$
More specific, I am curious to why we get an 4 and an 8. What formula or equation are being used to get those numbers? I know that the Laplace Transform calculates it for us, however, I want to calculate it "by hand" and show why we get the answer. Any feedback would be gladly appreciated!
Note that $(s+4)*(s+8) = s^2+12s+32$.