Factor the expression. Express your answer so that only positive exponents occur.
\[
2(2 x+5)^{3 / 5}(3 x+4)^{12 / 7}+3(2 x+5)^{8 / 5}(3 x+4)^{5 / 7}
\]
The factored expression is
(Simplifgryour answer. Use positive exponents only. Type your answer in factored form.)

Step 1 ：First, we observe that both terms in the expression have common factors of $(2x+5)$ and $(3x+4)$, each raised to a certain power.

Step 2 ：We can factor out the common factors by taking the lowest power of each common factor from each term. The lowest power of $(2x+5)$ is $\frac{3}{5}$ and the lowest power of $(3x+4)$ is $\frac{5}{7}$.

Step 3 ：So, we factor out $(2x+5)^{\frac{3}{5}}(3x+4)^{\frac{5}{7}}$ from each term, we get: \[(2x+5)^{\frac{3}{5}}(3x+4)^{\frac{5}{7}}[2+(2x+5)^{\frac{5}{5}}(3x+4)^{-\frac{2}{7}}3]\]

Step 4 ：Simplify the expression inside the brackets, we get: \[(2x+5)^{\frac{3}{5}}(3x+4)^{\frac{5}{7}}[2+3(2x+5)(3x+4)^{-\frac{2}{7}}]\]

Step 5 ：So, the factored expression is \[\boxed{(2x+5)^{\frac{3}{5}}(3x+4)^{\frac{5}{7}}[2+3(2x+5)(3x+4)^{-\frac{2}{7}}]}\]