How many common tangents can be drawn to the following circles $x^2+y^2=6x$ and $x^2+y^2+6x+2y+1=0?$

The coordiantes of the centres of the given circles are: $C_1(3,0),C_2(-3,-1)$ and corresponding radii are $r_1=3$ and $r_2=3,$ respectively.

Now, $C_1{C}_2=\sqrt{37}>r_1+r_2$

So, 4 common tangents can be drawn to the given circles.