Determine all possible rational solutions of the polynomial equation. \[ x^{3}+15 x^{2}+20 x+6=0 \] The list of all the possible rational solutions is (Simplify your answer. Use a comma to separate answers as needed.)

Step 1 ：By the Rational Root Theorem, the only possible rational roots are of the form \(\pm \frac{a}{b}\), where \(a\) divides 6 and \(b\) divides 1.

Step 2 ：Thus, the possible rational roots are \[\pm 1, \pm 2, \pm 3, \pm 6.\]

Step 3 ：Checking these values, we find that the rational roots are \(\boxed{-1,-2,-3}\).