Given the polynomial function P(x) = (2x - 6)(x + 4) - (x - 3)2 + (5x - 15).

Notice that $(2x - 6) = 2(x - 3)$ and $(5x - 15) = 5(x - 3)$.
Substitute these into the expression for $P(x)$:

The polynomial $P(x)$ as a product of its linear factors is $\boxed{(x - 3)(x + 16)}$.

The polynomial $P(x)$ in descending powers of $x$ is $\boxed{x^2 + 13x - 48}$.

The solutions are $\boxed{x = 3, x = -16}$.

The roots are $x = 3$ and $x = -16$, as found in part e).

The expression $(x - 3)(x + 16)$ is a parabola opening upwards (since the coefficient of $x^2$ is positive when expanded). This means the parabola is above or on the x-axis when $x$ is less than or equal to the smaller root, or greater than or equal to the larger root.
So, we need $x \le -16$ or $x \ge 3$.

The range of values for $x$ is $\boxed{x \le -16 \text{ or } x \ge 3}$.
In interval notation, this is $\boxed{(-\infty, -16] \cup [3, \infty)}$.