I'm a little confused on a quite simple quadratic problem. I need to calculate the maximum of $d(12-d)$ using basic quadratics. The answer is $6$ as can also be shown by $f'(x)= -2d +12$, however this is algebra not calculus. Using the squares method I get twelve, I think I may be using the incorrect method. Could someone set me on the right track?
$= -d^2 + 12d$
$-d^2 + 12/(-2)d + 36 = 36 $
$(d-6)^2 = 36$
$d = 12 or 0$ <- I understand these are the roots, am I not meant to calculate them?
The suggested answer is: $-(d-6)^2 + 36$, but I have no idea where it came from.