As with most quadratic equations, we can solve this equation by factoring the left side x² + 40x + 336
To factor this, we must find two values that have a sum 40 and a product of 336.
This might prove a little tricky for many.
We can factor this left side to get (x+12)(x+28)=0, which means x = -12 or x = -28

Answer: B

Here's an alternative approach (testing values) that isn't as time-consuming as we might first think.
In fact, if we recognize that the correct answer must be NEGATIVE, then we can solve this quickly.

How do I know that x must be NEGATIVE?
Well, if x is POSITIVE, then each term in the expression x² + 40x + 336 will evaluate to be POSITIVE
That is, if x is POSITIVE, then x² is POSITIVE, and 40x is POSITIVE
So, if x is POSITIVE then x² + 40x + 336 = POSITIVE + POSITIVE + 336
As you can see, if x is POSITIVE, then it's impossible for x² + 40x + 336 to equal 0
So, we can ELIMINATE answer choices C, D and E

At this point, we only need to test ONE of the two remaining answer choices.
If we test A and it works, then we're done. The correct answer is A.
If we test A and it doesn't work, then we're done. The correct answer is B.

So, let's test A (x = -6).
Replace x with -6 to get: (-6)² + 40(-6) + 336 = 0
Simplify: 36 - 240 + 336 = 0
Evaluate: 132 = 0
DOESN'T WORK
So, ELIMINATE A

Answer: B

Cheers,
Brent