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Sure, I can help solve these equations step-by-step. Let's solve each of them:

### (a) \((x - 2)(x - 3) = 0\)
To solve this, we use the zero-product property:
\[
(x - 2) = 0 \quad \text{or} \quad (x - 3) = 0
\]
So,
\[
x = 2 \quad \text{or} \quad x = 3
\]

### (b) \((x + 1)(x + 2) = 0\)
Using the zero-product property:
\[
(x + 1) = 0 \quad \text{or} \quad (x + 2) = 0
\]
So,
\[
x = -1 \quad \text{or} \quad x = -2
\]

### (c) \(x^2 - 9 = 0\)
This is a difference of squares:
\[
x^2 - 9 = (x - 3)(x + 3) = 0
\]
Using the zero-product property:
\[
(x - 3) = 0 \quad \text{or} \quad (x + 3) = 0
\]
So,
\[
x = 3 \quad \text{or} \quad x = -3
\]

### (d) \(x^2 - 25 = 0\)
This is another difference of squares:
\[
x^2 - 25 = (x - 5)(x + 5) = 0
\]
Using the zero-product property:
\[
(x - 5) = 0 \quad \text{or} \quad (x + 5) = 0
\]
So,
\[
x = 5 \quad \text{or} \quad x = -5
\]

### (e) \(x^2 + 4x = 0\)
Factor out \(x\):
\[
x(x + 4) = 0
\]
Using the zero-product property:
\[
x = 0 \quad \text{or} \quad (x + 4) = 0
\]
So,
\[
x = 0 \quad \text{or} \quad x = -4
\]

### (f) \(x^2 + 3x = 0\)
Factor out \(x\):
\[
x(x + 3) = 0
\]
Using the zero-product property:
\[
x = 0 \quad \text{or} \quad (x + 3) = 0
\]
So,
\[
x = 0 \quad \text{or} \quad x = -3
\]

### (g) \(x^2 - 3x = 0\)
Factor out \(x\):
\[
x(x - 3) = 0
\]
Using the zero-product property:
\[
x = 0 \quad \text{or} \quad (x - 3) = 0
\]
So,
\[
x = 0 \quad \text{or} \quad x = 3
\]

### (h) \(x^2 + x = 0\)
Factor out \(x\):
\[
x(x + 1) = 0
\]
Using the zero-product property:
\[
x = 0 \quad \text{or} \quad (x + 1) = 0
\]
So,
\[
x = 0 \quad \text{or} \quad x = -1
\]

Would you like more details on any of these steps? If you have any questions, feel free to ask!

Here are 5 questions you might consider asking:
1. How do you solve quadratic equations using the quadratic formula?
2. What are the different methods to factor quadratic equations?
3. How do you solve higher degree polynomial equations?
4. What is the difference between solving equations algebraically and graphically?
5. Can you explain how to complete the square to solve a quadratic equation?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

Explore step-by-step solutions to solve quadratic equations such as (a) (x - 2)(x - 3) = 0, (b) (x + 1)(x + 2) = 0, and more. Understand key algebraic concepts like the quadratic equation formula and the zero-product property. Ideal for high school students.

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