For which values of $x$ is the product $(x-4)\left(x^{2}-9 x+20\right)$ positive?
The product can also be written as:

$$
(x-4)(x-4)(x-5)
$$

or

$$
(x-4)^{2}(x-5)
$$

This expression is positive when $x>5$.

Number of solutions: 24.