Your original mean is 20. So subtract 20 from all the numbers to get a mean of 0.
Your original std deviation is 5, So scale by 1/5 to reduce the std deviation to 1.
These combine to a transformation of (1/5)x -20.
The random variable T has the:
Standard deviation 5
It is required to scale T by using the transformation S = aT + b where a and b are constants ( a > 0 ) so that E ( S ) and Var ( S ) satisfy specified values.
Find the value of a and b in this particular case:
when E ( S ) = 0
and when Var ( S ) = 1
The standard language is such that +B means add some constant. There is no constraint that the constant be positive unless the language says "add a positive constant". So negatives are fine. In the future, you might have to add a complex number, which is neither positive nor negative.