3. Solve the equation

$$
3 \sqrt{6 x^{2}+13 x+5}-6 \sqrt{2 x+1}-\sqrt{3 x+5}+2=0
$$
Solution. Note that $6 x^{2}+13 x+5=(2 x+1)(3 x+5)$. Introduce the notations: $\left\{\begin{array}{l}m=\sqrt{2 x+1} ; n=\sqrt{3 x+5} . \\ m \geq 0 \\ n \geq 0\end{array}\right.$

Then the equation can be represented as $3 m n-6 m-n+2=0$.

Considering the domain of definition, solve this equation:

$3 m(n-2)-(n-2)=0 \Rightarrow(3 m-1)(n-2)=0 \Rightarrow m=1 / 3, n=2$.

Return to the variable $x\left[\begin{array}{l}\sqrt{2 x+1}=1 / 3 ; \\ \sqrt{3 x+5}=2 ;\end{array} \Rightarrow\left[\begin{array}{l}2 x+1=1 / 9 ; \\ 3 x+5=4 ;\end{array} \Rightarrow\left[\begin{array}{l}x=-4 / 9 ; \\ x=-1 / 3 ;\end{array}\right.\right.\right.$

Answer: $-1 / 3 ;-4 / 9$