Hi bournouli,

sorry for any misunderstanding about the 'positive' conclusion; it just could simplify the factorization for us but not necessarily to enforce a '+' sign.

Just reread ur post, now I guess I find where u went wrong:

you transformed the original equation to -8(-h^2+3H+40)=0, it's ok for the '-h^2';

now suppose the factorization result is (-h+a)(h+b)=0

spread it we'll get -h^2++(a-b)h+ab=0; compare it with -h^2+3H+40=0

then we get two equations: a-b=3, ab=40 (exactly where u went wrong, as u considered ab=-40 in ur post)

a=8, b=5.

back to (-h+a)(h+b)=0, two solutions should be h=a or h=-b, i.e., h=8, or h=-5.

hope it's clear for u now