One of the keys here is to see that there is a quadratic that cannot be factored out (or in other words, broken down) "nicely".

This should raise a red flag, and alert the test taker that something "clever" can be done. For example, the second equation of x^2−12x+40 = ? can not be broken down into integers, like what we may be use to. When you hit this point, stop and look at the other equation and then be on the look out for something clever to do.

With equation x/4=(5x−2)/(x+8), I cross multiply to remove the denominators. The result is x^2 -12x +40 = 32.

Here I notice that now both equations have x^2 -12x, and this is the big clue. So I rearrange this equation to be x^2 -12 = -8, and now I see replace x^2 -12 in the equation x^2−12x+40 = ? with -8, so it become (-8)
+40 = ?. Completing -8 + 40 = ?, results in 32.

Choice E is the answer.