ANSWER
[tex]n = 8 \: or \: n = - 2[/tex]
EXPLANATION
The given function is
[tex]f(n) = {n}^{2} - 6n - 16[/tex]
To find roots of the equation, we set the equation to zero.
[tex]{n}^{2} - 8n + 2n- 16 = 0[/tex]
Split the middle term with -8n+2n
We now factor to get,
[tex]n(n - 8) + 2(n- 8) = 0[/tex]
[tex](n - 8)(n + 2) = 0[/tex]
Using the zero product property,
[tex]n - 8 = 0 \: or \: n + 2 = 0[/tex]
[tex]n = 8 \: or \: n = - 2[/tex]
