If the center lies on the x axis, call the center (a, 0)
So.....the distance from this point to each of the given points is equal
So....equating distances, we have that
(-3-a)^2 + ( 2 -0)^2 = (-2-a)^2 + (3-0)^2 simplify
((-1) (3 + a))^2 + 2^2 = ((-1)(2 + a))^2 + 3^2
(3 + a)^2 + 4 = (2 + a)^2 + 9
9+ 6a + a^2 + 4 = 4 + 4a + a^2 + 9 subtract a^2 from both sides and simplify
6a +13 = 4a + 13 subtract 13 from both sides
6a = 4a
This is true when a = 0
So the center is (a, 0) = (0, 0)
And the radius is sqrt [ ( 0 - -3)^2 + (0 -2)^2 ] = sqrt [ 3^2 +2^2] = sqrt ( 13)
Here's a graph : https://www.desmos.com/calculator/dd6nbqzagb