Question 233174
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Basically, if a * b = 0, then either a = 0 or b = 0 or both.


Your problem is:


n^2+7n+6=0


This can be factored to become:


(n+6) * (n+1) = 0


This means that either (n+6) must equal zero, or (n+1) must equal 0.


If n+6 = 0, this means that n = -6
If n+1 = 0, this means that n = -1


Your answer is that n = -6 or n = -1


You then test these solutions in your original equation to see if they are true.


If n = -1, then n^2 + 7n + 6 = becomes (-1)^2 + 7*(-1) + 6 = 0 becomes 1 - 7 + 6 = 0 becomes 0 = 0.


Since the equation is true, n = -1 is a good answer.


If n = -6, then n^2 + 7n + 6 becomes (-6)^2 + 7(-6) + 6 = 0 becomes 36 - 42 + 6 = 0 becomes -6 + 6 = 0 becomes 0 = 0.


Since the equaion is true, n = -6 is a good answer also.


Your answer is that n can be either -1 or -6 as long as there are no restrictions on whether n can be negative or not.  That depends on what n represents.  In this particular problem, it doesn't represent anything that can't be negative so your answer is valid.