6.361 Solve the equation $a x^{3}+b x^{2}+c x+d=0$, if its coefficients $a, b, c, d$ in the given order form a geometric progression with a given common ratio $q$.
Solution. The original equation can be written as:

$$
\begin{aligned}
& a x^{3}+a q x^{2}+a q^{2} x+a q^{3}=0 \Leftrightarrow x^{3}+q x^{2}+q^{2} x+q^{3}=0 \Leftrightarrow \\
& \Leftrightarrow(x+q)\left(x^{2}+q^{2}\right)=0 \Leftrightarrow x=-q .
\end{aligned}
$$

Answer: $x=-q$.