6c-1 = 0
6c=1
c=1/6
For absolute value, you also have to consider the negative of what's inside the bars, because |x| = x if x is positive, and -x if x is negative.
-(6c-1) = 0
-6c +1 = 0
-6c=-1
c = 1/6
When the absolute value is = 0, the solution will always be the same, because the graph of |ac+y| is a v that meets at y=0