If x degrees Fahrenheit = nx degrees Celsius, where each of n and x is a nonzero integer, determine all values of n and x for which this is possible.

Keeping all the other conditions unaltered, how about:
x degrees Celsius = nx degrees Fahrenheit?

Note:
Fahrenheit to Celsius:
^oC= 5*(^oF - 32)/9

Celsius to Fahrenheit :
^oF= (°C*9/5) + 32