Question

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

Answer 1

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

Answer 2

n = 1

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