How to use the rational root theorem to list all possible rational roots?

${\displaystyle f\left(x\right)=a_0{x}^n+a_1{x}^{n-1}+...+a_{n-1}x+a_n}$
Any rational roots of f(x) = 0 may be expressed in lowest terms as ${\displaystyle \frac{p}{q}}$, where p, ${\displaystyle p,q\in \mathbb{Z}}$, ${\displaystyle q\ne 0}$, p is a divisor of ${\displaystyle a_n}$, and q is a divisor of ${\displaystyle a_0}$. To discover all the distinct fractions ${\displaystyle \frac{p}{q}}$ that arise, list all the possible integer factors of ${\displaystyle a_0}$ and ${\displaystyle a_n}$, then all the potential rational roots. Consider the case when ${\displaystyle f\left(x\right)=6x^3-12x^2+5x+10}$
${\displaystyle a_n=10}$ has factors +-1, +-2, +-5 and +-10. (possible values of p); ${\displaystyle a_0=6}$ has factors +-1, +-2, +-3 and +-6. (possible values of q)
Possible fractions:
+-1/6, +-1/3, +-1/2, +-2/3, +-5/6, +-1, +-5/3, +-2, +-5/2, +-10/3, +-5, +-10