https://file.aiquickdraw.com/mathbot/file/1724814495796uz4tycvd.jpg

The provided image shows the equation:

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

To solve this equation using factoring, we apply 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. Therefore, we can set each factor equal to zero:

1. \( x - 3 = 0 \)
2. \( x + 4 = 0 \)

Now, solve each equation:

1. \( x - 3 = 0 \)  
   \( x = 3 \)

2. \( x + 4 = 0 \)  
   \( x = -4 \)

The solutions to the equation are:

\[
x = 3 \quad \text{or} \quad x = -4
\]

These are the values of \( x \) that satisfy the given quadratic equation.

Would you like more details on this process, or do you have any questions?

Here are five related questions for further practice:

1. How would you solve the equation \((x - 5)(x + 2) = 0\)?
2. What are the solutions to the equation \((x + 6)(x - 1) = 0\)?
3. How can you apply the zero product property to solve \((x + 1)(x - 7) = 0\)?
4. Can you solve the equation \((2x - 3)(x + 5) = 0\) using the zero product property?
5. How would you factor and solve the equation \(x^2 - 7x + 10 = 0\)?

**Tip:** When dealing with quadratic equations in the form \((x-a)(x-b) = 0\), set each factor equal to zero separately to find the solutions.

Learn how to solve the quadratic equation (x - 3)(x + 4) = 0 using factoring and the zero product property. This problem covers key algebraic concepts, including quadratic equations, factoring methods, and the zero product property theorem. Suitable for students in Grades 9-12.

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