Example 3. Solve the equation

$$
5^{2 x+1}-3 \cdot 5^{2 x-1}=550
$$
Solution. Factoring out the expression $5^{2 x-1}$ on the left side of the equation, we get

$$
5^{2 x-1}\left(5^{2}-3\right)=550 \Leftrightarrow 5^{2 x-1}=5^{2} \Leftrightarrow 2 x-1=2 \Leftrightarrow x=3 / 2
$$