Here are the solutions for each part:

(a) Solve $f(x) = 0$:
The solutions are $x = -3$ and $x = 6$.

(b) Solve $g(x) = 0$:
The solutions are $x = -6$ and $x = 3$.

(c) Solve $f(x) = g(x)$:
The solution is $x = 0$.

(d) Solve $f(x) > 0$:
The solution is $x \in (-\infty, -3) \cup (6, \infty)$.

(e) Solve $g(x) \leq 0$:
The solution is $x \in [-6, 3]$.

(f) Solve $f(x) > g(x)$:
The solution is $x \in (-\infty, 0)$.

(g) Solve $f(x) \geq 2$:
The solution is $x \in (-\infty, \frac{3}{2} - \frac{\sqrt{89}}{2}] \cup [\frac{3}{2} + \frac{\sqrt{89}}{2}, \infty)$.

Would you like further details on any of these solutions?

Here are five related questions for practice:

1. What are the intervals where $g(x) > 0$?
2. How do the graphs of $f(x)$ and $g(x)$ compare?
3. What are the vertex points of both $f(x)$ and $g(x)$?
4. Can you determine the axis of symmetry for each function?
5. How would $f(x) \geq g(x)$ be solved?

Tip: When solving inequalities, always remember to test the critical points where the expressions are equal, as these can help determine the correct intervals.