To solve the equation \((2x + 7)(x - 1) = 0\), we can use the **Zero Product Property**, which states that if the product of two factors is zero, then at least one of the factors must be zero. This gives us two separate equations to solve:

1. \(2x + 7 = 0\)
2. \(x - 1 = 0\)

### Step 1: Solve the first equation
\[
2x + 7 = 0
\]
Subtract 7 from both sides:
\[
2x = -7
\]
Divide both sides by 2:
\[
x = -\frac{7}{2}
\]

### Step 2: Solve the second equation
\[
x - 1 = 0
\]
Add 1 to both sides:
\[
x = 1
\]

### Final Answer
The solutions to the equation are:
\[
x = -\frac{7}{2} \quad \text{or} \quad x = 1
\]

Would you like more details or have any questions?

Here are some related questions:
1. What if one of the factors was a quadratic equation?
2. How do you solve quadratic equations by factoring?
3. What happens when both solutions of the factors are the same?
4. Can you explain the Zero Product Property in detail?
5. How does this method compare with using the quadratic formula?

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

Learn how to solve the equation (2x + 7)(x - 1) = 0 with a detailed step-by-step solution. Understand the application of the Zero Product Property in solving algebraic equations. Suitable for students in Grades 7-9.

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