QM- Why is the separation constant +/-l(l+1) ?

[jinksys]

This isn't a HW problem, it's more of a general question. I'm reading Griffith's Intro to QM 3rd Edition. On page 134 he uses separation of variables, of which I'm familiar (but by no means an expert). Could someone explain why the separation constant in equations 4.16 and 4.17 changes sign?

The equations in question : http://imgur.com/8OKqz"

 

[vela]

If you look at the equation above those two, you see the terms sum to 0, so if one is positive, the other one is negative.

 

[jinksys]

If you look at the equation above those two, you see the terms sum to 0, so if one is positive, the other one is negative.

Jeez, that should have been obvious!
Thanks for your help.