To multiply rational expressions involving trinomials, such as $\frac{3a^2-8a-3}{a^2-25} \cdot \frac{a^2+10a+25}{3a^2-14a-5}$, first factor all numerators and denominators completely to obtain $\frac{(3a+1)(a-3)(a+5)(a+5)}{(a-5)(a+5)(3a+1)(a-5)}$. Then, simplify the expression by dividing out the common factors $(3a+1)$ and $(a+5)$, which leaves $\frac{(a-3)(a+5)}{(a-5)(a-5)}$. Finally, rewrite any repeated factors using an exponent, resulting in the simplified product $\frac{(a-3)(a+5)}{(a-5)^2}$.