I need to find the value of n if the graph of f(x)=n*x+n-4 is passing through the point A(n,-2).

If the point A lies on the graph of the given function,
it's coordinates must verify the equation of the
function.

A(n,-2) belongs to graph of f(x)
<=> f(n) = n*n + n - 4 = -2

We'll compute
f(n):

n^2 + n - 2 = 0

We'll
apply quadratic formula:

n1 = [-1 + sqrt(1 +
8)]/2

n1 = (-1 + 3)/2

n1 =
1

n2 = (-1 - 3)/2

n2 =
-2

Since there are no conditions imposed concerning the
nature of the value of n, we'll keep them both, therefore there are two points that may
be located on the graph of f(x): (1 ; -2) and (-2 ,
-2).

The requested values for n are: {-2 ;
1}.