N (n - 4) + n (n + 8) = n (n - 13) + n (n + 1) + 16

N^2 - 4n + n^2 + 8n = n^2 - 13n + n^2 + n + 16

-4n + 8n = - 13n + n + 16

-4n = - 12n + 16

4n + 12n = 16

16 = 16

n = 1

n = 1

Step-by-step explanation:

n (n - 4) + n (n + 8) = n (n - 13) + n (n+1) + 16

n^2 - 4n + n^2 + 8n = n^2 - 13n + n^2 + n + 16

n^4 + 4n = n^4 - 12n + 16

n^4 - n^4 + 4n + 12n - 16 = 0

16n - 16 = 0

16n = 16

n = 16/16

n = 1

better check this ...

1 (1 - 4) + 1 (1 + 8) = 1 (1 - 13) + 1 (1 + 1) + 16

1 (-3) + 1 (9) = 1 (-12) + 1 (2) + 16

-3 + 9 = - 12 + 2 + 16

6 = 4 + 2

6 = 6 (correct) ... so it checks out