Example 2. Solve the inequality

$$
(0.1)^{4 x^{2}-2 x-2} \leqslant(0.1)^{2 x-3}
$$
Solution. The given inequality is equivalent to the inequality

$$
4 x^{2}-2 x-2 \geqslant 2 x-3 \Leftrightarrow 4 x^{2}-4 x+1 \geqslant 0 \Leftrightarrow(2 x-1)^{2} \geqslant 0
$$

Thus, the original inequality is satisfied by all real numbers.

When solving some exponential inequalities, a transformation is used that involves factoring out a common factor.