Answer
$r=-4 \cos \theta$
Work Step by Step
Here, we have $x^2+y^2+4x=0$
This implies that
$(x+2)^2+y^2=4$
Thus, we have an equation of a circle with center $(-2,0)$ and radius $2$
So, $r^2+4r \cos \theta=0$
Hence, $r=-4 \cos \theta$