SOLUTION: Solve the equation: (n+6)!/(n+4)!=12 Here is what I have done so far: (n+6)!/(n+4)!=12 (cross multiply) (n+6)!/(n+6)!=12/1 0= 12(n+4)!(n+5)!(n+6)!/ (n+6)! (The (n+6)

Question 272184: Solve the equation: (n+6)!/(n+4)!=12
Here is what I have done so far:
(n+6)!/(n+4)!=12 (cross multiply)
(n+6)!/(n+6)!=12/1
0= 12(n+4)!(n+5)!(n+6)!/ (n+6)! (The (n+6)!'s cancel out with each other)
0= (n+4) (n+5) (this is the result when you divide 12 by both sides)
I don't know where to go from here. Did I make an error? or does n= -4 and n=-5 ?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
[(n + 6) (n + 5) (n + 4) (n + 3)...] / [(n + 4) (n + 3)...] = 12

(n + 6) (n + 5) = 12

n^2 + 11n + 30 = 12

n^2 + 11n + 18 = 0

(n + 9) (n + 2) = 0

n = -9 ___ AND ___ n = -2

negative factorials are not defined, so n = -2
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