if product of some of natural numbers n,n+1,n+2,n+3,n+4 & n+5 equal to the product of the remaining find n=?

Question

if product of some of teh natrural numbers out of n, n+1,n+2,n+3,N+4 and n+5 be equal to the product of remaining, find the value of n
i.e. n *(n+2)*(n+4) = (n+5)*(n+3)*(n+1)
find n=?
n is the natural number

Answer 1

n(n^2+6n+8)=(n+5)(n^2+4n+4)
n^3+6n^2+8n=n^3+9n^2+24n+20
3n^2+16n+20=0
(3n+10)(n+2)=0
n=-2 or -10/3
so n(n+2)(n+4) cannot be equal to (n+5)(n+3)(n+1)
if n is a natural number

Answer 2

5 is a factor of at least one of the numbers. so it must appear twice. Hence n is a multiple of 5. And since 7 cannot be a factor in two of the numbers, it is a factor in none. Therefore n must be of the form 7p +1.

Well all of this is bullshit.: there is no solution.