any algebraic equation with absolute value must be rewritten in its positive and negative form without the absolute value.
|x| = 6 so
x = 6 and x = -6
|x-3| = 5 becomes
x-3 = 5 and x-3 = -5 so
x=8 and x=-2, and both work when you plug them back in.
Same thing here.
Start with |b+6|-|b-5|=0, and make it
So b+6 = b-5 or b+6 = -(b-5)
Solve each one, and see that in the first one, b cancels and it's impossible, and in the second one, b=-.5
Taking time in to consideration, this will be the quickest method to solve the problem