-1-|x+5|=-14 is an absolute value equation. It transforms into two separate equations with different solutions:
First multiply all three terms by -1. This results in 1 + |x+5| = 14, or |x+5| = 13.
There are two cases here. The first is when x+5 is already +. Here the absolute value operator doesn't make any difference:
x+5 = 13. Subtracting 5 from both sides, we get x = 8.
The second case is when (x+5) is negative. Applying the absolute value sign produces the result -(x+5). Note that neg times neg equals pos. Now write out -(x+5) = 13 and solve for x: -x - 5 = 13, or x = -18.
The solutions are {-18,8}.