To solve the equation \(\left(x - 3\right)\left(x + 4\right) = 0\), we can use the zero-product property. This property states that if the product of two factors is zero, then at least one of the factors must be zero.

### Steps:

1. **Set each factor equal to zero:**

   \[
   x - 3 = 0
   \]
   \[
   x + 4 = 0
   \]

2. **Solve for \(x\) in each equation:**

   - For \(x - 3 = 0\):
     \[
     x = 3
     \]

   - For \(x + 4 = 0\):
     \[
     x = -4
     \]

### Solution:

The solutions to the equation \(\left(x - 3\right)\left(x + 4\right) = 0\) are \(x = 3\) and \(x = -4\).

Would you like further details or have any questions?

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Here are 5 related questions for further practice:

1. Solve the equation \(\left(x + 2\right)\left(x - 5\right) = 0\).
2. What are the solutions to \(\left(2x - 1\right)\left(x + 3\right) = 0\)?
3. How do you solve the quadratic equation \(\left(x + 7\right)\left(x - 2\right) = 0\)?
4. If \(\left(3x + 4\right)\left(x - 6\right) = 0\), what are the solutions for \(x\)?
5. Solve for \(x\) in the equation \(\left(x - 1\right)\left(x + 8\right) = 0\).

**Tip:** The zero-product property is a quick way to solve quadratic equations that can be factored into linear expressions.

Learn how to solve the equation (x - 3)(x + 4) = 0 step-by-step using the zero-product property. Understand the principles of algebra and the application of the zero-product property in solving quadratic equations. Suitable for students in Grades 7-9.

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