40 below.
F = (9/5) C + 32
-40 = -(9/5)*40 + 32
-40 = -(9*40/5) + 32
-40 = -(9*8) + 32
-40 = -72 +32
-40 = -40
I've never experienced it, coldest I dealt with was -28 F in Minneapolis.
The lowest temperature I saw in Great Falls, MT was -38 when I lived there (1977 - 79). I experienced wind chill temperatures of -70 or more a couple of times during my two winters there. My 1967 Dodge pickup still started at -38. I did not have a plug in heater attached to the front.
or
F=(9/5)C+32
Let F=C
C=(9/5)C+32
-(4/5)C=32
C=-32(5/4)
C=-40
F=C=-40