need help to reverse the direction of a brushless motor

JimboZA:
Just yesterday I tried to run a laptop cooling fan backwards by hooking the battery up back-to-front, and it didn't start.

Do brushless DC motors actually even run backwards?

A brushless fan as found in a computer contains the controller within the fan and that controller is only designed to spin the fan in one direction. Fundamentally though, brushless DC motors are certainly reversible.

FWIW there are zillions of RC cars with brushless motors and reverse capability.