7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.
Solution.

Write the equation as

$$
\begin{aligned}
& \frac{5^{2 x}}{5}-5^{2 x}=-2^{2 x}-4 \cdot 2^{2 x},-\frac{4}{5} \cdot 5^{2 x}=-5 \cdot 2^{2 x} \\
& \left(\frac{5}{2}\right)^{2 x}=\left(\frac{5}{2}\right)^{2}, x=1
\end{aligned}
$$

Answer: 1.