BJTs - Large DC Signal Analysis - Negative Voltages
There is really only one trick here- to find out whether the BE junction is forward biased or not. Just like you'd do with a diode, imagine the base connection open and what voltage would appear there- is it more than 0.7V? Since it is (it looks like it would be about +5V) we can assume the junction is conducting, and thus the base voltage is fixed at 0.7V. 

Now it's straightforward to calculate the base current as (15-0.7)/470K + (-15-0.7)/1M. 

If you swapped the two base resistors, you'd have the opposite situation and could simply ignore the base and calculate the base voltage as if it was a simple voltage divider.