Looks like you got a typo, the equation must be: [tex]x^2+y^2+6x-4y+12=0[/tex]
To solve it:
First, rewrite it in the form of a standard circle equation.
[tex]\left(x-\left(-3\right)\right)^2+\left(y-2\right)^2=1^2[/tex]
Then, we know the answer:
The center is found at: [tex]\left(-3,\:2\right)[/tex]
[tex]r=1[/tex]
Have a nice day! :)
