If the whole coefficient equation has a rational root, the denominator of the rational root is the divisor of the highest coefficient, and the numerator is the divisor of the constant term. So, if you try a few and simplify them, you can usually solve them.

Or:

Guess an answer first, then divide it vertically, and three times will become two times, and that's all. . .

There must be a good guessing solution to the cubic equation in high school. .