The word "both" has two distinct meanings that I'm aware of:
(a) if you want to express "P(A) and P(B)" for some predicate P, one says "both A and B P" (if A,B are subjects) or "P both A and B" (if A,B are objects).
e.g.<< On the third day, both groups successfully recalled the link between the shock and the spider. >>
(b) A ~ B, where ~ is an equivalence relation.
e.g.:<< On the third day, both groups remembered the link between the shock and the spider equally well >>
I really dislike usage (b), and I'd recommend using "the two" instead. It feels so wrong that I was unable to generate an example myself, and had to find the webpage again.
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UPDATE: a curious variant of (b) is
"both equally as".