GIVEN: ax(cx + d) = -b(cx + d)
Add b(cx + d) to both sides to get: ax(cx + d) + b(cx + d) = 0
Rewrite as: (ax + b)(cx + d) = 0

This means either (ax + b) = 0 or (cx + d) = 0
Let's examine each case

Case a: ax + b = 0
So: ax = -b
Solve: x = -b/a

Case b: cx + d = 0
So: cx = -d
Solve: x = -d/c

Which of the following is a possible ratio of the 2 solutions?
ASIDE: Why does the question ask for a POSSIBLE ratio?
Well, the ratio of the solutions can be EITHER (-b/a)/(-d/c) OR (-d/c)/(-b/a)

Let's check the first ratio.
(-b/a)/(-d/c) = (-b/a)(c/-d) = bc/ad check the answer choices . . . not there.
However, answer choice E is the reciprocal of bc/ad, so it must be the correct answer.

Not convinced?
Let's confirm.
(-d/c)/(-b/a) = (-d/c)(a/-b) = ad/bc = answer choice E

Cheers,
Brent