How do I solve this multi variable equation for all the values of x and the value of r-s? 4x^2+20x+r=(2x+s)^2

You can express x in terms of r and s as though r and s are constants.

To do this, you need to expand the right-hand side and the two 4x² terms will cancel out. Transpose and express x in terms of r and s:
x=-(s²-r)/(4s-20)