13. As shown in Figure 4, in the Cartesian coordinate system, there are four points $A(-2,4) 、 B(-2,0) 、 C(2,-3) 、 D(2,0)$. Let $P$ be a point on the $x$-axis, and the triangle formed by $P A 、 P B 、 A B$ is similar to the triangle formed by $P C 、 P D 、 C D$. Write down the coordinates of all points $P$ that satisfy the above conditions $\qquad$
$$
\frac{P B}{A B}=\frac{P D}{C D} \text { or } \frac{P B}{A B}=\frac{C D}{P D} ,
$$

i.e., $\frac{|x+2|}{4}=\frac{|x-2|}{3}$ or $\frac{|x+2|}{4}=\frac{3}{|x-2|}$.
Solving, we get $x=-4, \frac{2}{7}, 14,4$.