SOLUTION: Dear math teacher, Would you please help me solve this problem? Find n if 3times {(2n+4)Permutation3} = 2times {(n+4)Permutation4} Here is what I got: 3 times (2n+4)

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Question 473539: Dear math teacher,
Would you please help me solve this problem?
Find n if
3times {(2n+4)Permutation3} = 2times {(n+4)Permutation4}
Here is what I got:
3 times (2n+4) times (2n+3) times (2n+2) = 2 times (n+4) times (n+3) times (n+2) times (n+1)
But then I am not sure how to isolate n on one side of the equation to solve for it. The correct answer is: 6.
Thank you very much for your time and effort in helping me with my homework.
I.
Answer by ccs2011(207) (Show Source):
You can put this solution on YOUR website!
Looks good so far!
To isolate n you need to multiply everything out, then simplify by adding like terms
You should end up with a 4th degree polynomial:

Now n must be a positive integer because we are dealing with a permutation.
Use synthetic division to try to factor out a factor of 12.
Try 1,2,3,4,6,12 these are the only possible solutions.
If you get a zero remainder then its the solution.