Since (-2,3) and (2,-1) lie on this circle, you get two equations for the coordinates u, v of the center, namely
If you now subtract the second equation from the first, you get , and hence .
Replacing in the first equation by gives you the quadratic equation .
Now solve for : this gives you two solutions for . Finally, pair these two solutions with the corresponding x-coordinates of C, namely , and you are done.