Let's solve the three equations shown in the image:

a. $(x - 4)(x - 5) = 0$

We apply the zero product property, which states that if the product of two factors is 0, then at least one of the factors must be 0.

1. $x - 4 = 0 \Rightarrow x = 4$
2. $x - 5 = 0 \Rightarrow x = 5$

So, the solutions are x = 4 and x = 5.

d. $(2x - 1)(x + 4) = 0$

Again, applying the zero product property:

1. $2x - 1 = 0 \Rightarrow 2x = 1 \Rightarrow x = \frac{1}{2}$
2. $x + 4 = 0 \Rightarrow x = -4$

So, the solutions are x = $\frac{1}{2}$ and x = -4.

g. $(x - 7)(x - 9) = 0$

Using the zero product property one more time:

1. $x - 7 = 0 \Rightarrow x = 7$
2. $x - 9 = 0 \Rightarrow x = 9$

So, the solutions are x = 7 and x = 9.

Would you like further explanations on any of these? Here are five related questions:

1. How does the zero product property work?
2. What happens when one side of the equation is not zero?
3. How would you solve a quadratic equation if it was not factored?
4. Can you graph these solutions on a number line?
5. What is the relationship between factoring and solving quadratic equations?

Tip: Always check if the equation can be factored easily before using more advanced methods to solve quadratics.