Write the equation of a circle with center (-2,3) and a radius of 4. show all work to receive credit.

The equation of the circle is given by:
(x-a)^2+(y-b)^2=r^2
where:
(a,b) is the center  of the circle
given that the center of our circle is (-2,3) with the radius of 4, the equation will be:
(x+2)^2+(y-3)^2=4^2
expanding the above we get:
x^2+4x+4+y^2-6y+9=16
this can be simplified to be:
x^2+4x+y^2-6y=16-13
x^2+y^2+4x-6y=3