https://file.aiquickdraw.com/mathbot/file/1728410425664y5ii6kxt.jpg

The equation shown in the image is:

\[
-4(x - 1)(2x - 5) = 0
\]

We can solve this equation using the Zero-Factor Property, which states that if the product of several factors is zero, at least one of the factors must be zero.

### Step-by-step solution:

1. **Divide both sides by -4** (since dividing by a non-zero constant doesn't affect the equality):
   \[
   (x - 1)(2x - 5) = 0
   \]

2. **Apply the Zero-Factor Property**:
   \[
   x - 1 = 0 \quad \text{or} \quad 2x - 5 = 0
   \]

3. **Solve each equation**:
   - For \(x - 1 = 0\):
     \[
     x = 1
     \]
   - For \(2x - 5 = 0\):
     \[
     2x = 5 \quad \Rightarrow \quad x = \frac{5}{2}
     \]

### Final Answer:
The solutions are:
\[
x = 1, \frac{5}{2}
\]

Would you like more details on this solution or have any specific questions?

### 5 Follow-up Questions:
1. What is the Zero-Factor Property, and why does it apply in this case?
2. How do we solve an equation after applying the Zero-Factor Property?
3. Why can we divide both sides of the equation by -4 without changing the solution?
4. What is the importance of factoring in solving quadratic equations?
5. How can we check if the solutions \(x = 1\) and \(x = \frac{5}{2}\) are correct?

### Tip:
Always check your solutions by substituting them back into the original equation to verify if both sides are equal.

Learn how to solve the equation -4(x - 1)(2x - 5) = 0 using the Zero-Factor Property. This algebra problem focuses on factoring and solving quadratic equations. Suitable for students in Grades 9-10.

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