7. The function $f(x)$ satisfies for all real numbers $x$:
$$
f(2-x)=f(2+x), f(5+x)=f(5-x) \text {, and } f(0)=0
$$

Then $f(x)$ has at least $\qquad$ zeros in the interval $[-21,21]$.
7. Since $f(x)=f(2+x-2)$
$$
\begin{array}{l}
=f(2-(x-2)) \\
=f(5-(x+1)) \\
=f(5+x+1)=f(6+x),
\end{array}
$$

thus $f(x)$ is a periodic function with a period of 6.
Also, since $f(0)=f(4)=0$, there are at least 2 zeros in one period, so the answer is 14.