I got a positive 13 instead of a -13 which is the correct answer. What did i do wrong?

The answer is -13
After you add the -13 to both sides, you end up with:
-n = 13
When you rewrote the problem, you got rid of the negative sign on the n variable, making it positive. If you kept the negative sign, you end up with -13 as a final result because you need to find n, not negative n.
Thus,
n = -13
Summary:
Your mistake was that you got rid of the negative sign on the n, changing the problem's answer.
:)
Answer:
You seemed to have forgotten the negative in front of the [tex]n[/tex]
Step-by-step explanation:
You seemed to have forgotten the negative in front of the [tex]n\\[/tex]
[tex]-13-n=0[/tex]
Move negative thirteen to the other side
[tex]-n=13[/tex]
Divide by negative one
[tex]n=-13[/tex]