https://file.aiquickdraw.com/mathbot/file/1726673814678x1dba3gb.jpg

The equation provided is:

\[
(5x + 6)(6x + 5) = 0
\]

To solve for \( x \), we apply the **Zero Product Property**, which states that if \( A \times B = 0 \), then either \( A = 0 \) or \( B = 0 \).

### Step 1: Set each factor equal to zero.

1. \( 5x + 6 = 0 \)
2. \( 6x + 5 = 0 \)

### Step 2: Solve each equation separately.

#### Equation 1: \( 5x + 6 = 0 \)

\[
5x = -6
\]

\[
x = -\frac{6}{5}
\]

#### Equation 2: \( 6x + 5 = 0 \)

\[
6x = -5
\]

\[
x = -\frac{5}{6}
\]

### Final Answer:

The solutions are \( x = -\frac{6}{5} \) or \( x = -\frac{5}{6} \).

Looking at the answer choices in the image:

- The correct option is **the second one**, which shows \( x = -\frac{6}{5} \) or \( x = -\frac{5}{6} \).

Would you like further details or have any questions?

Here are some related questions to further explore the topic:

1. How can you apply the Zero Product Property to quadratic equations in general?
2. What does it mean if both factors in the product are the same?
3. How would the equation change if it were written as \( (5x - 6)(6x + 5) = 0 \)?
4. Can this problem be solved graphically? If so, how?
5. What would happen if we multiplied out the terms before solving?

**Tip:** Always check both solutions by substituting them back into the original equation to ensure correctness.

Learn how to solve the equation (5x + 6)(6x + 5) = 0 using the Zero Product Property. This problem covers key algebraic concepts such as factoring and solving linear equations, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation