https://file.aiquickdraw.com/mathbot/file/1725998666576n5avzrcs.jpg

The equation shown in the image is:

\[
(3w - 4)(6 + w) = 0
\]

To solve this equation, we apply the **Zero-Product Property**, which states that if the product of two factors is zero, at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for \( w \).

1. Set the first factor equal to zero:
   \[
   3w - 4 = 0
   \]
   Solving for \( w \):
   \[
   3w = 4 \quad \Rightarrow \quad w = \frac{4}{3}
   \]

2. Set the second factor equal to zero:
   \[
   6 + w = 0
   \]
   Solving for \( w \):
   \[
   w = -6
   \]

Thus, the two solutions for \( w \) are:
\[
w = \frac{4}{3}, \, w = -6
\]

You should enter these two solutions separated by a comma: `w = 4/3, -6`.

Would you like further details on the steps, or do you have any other questions?

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Here are 5 related questions:
1. What is the Zero-Product Property, and how does it apply to factored equations?
2. How do you factor quadratic equations into two binomials?
3. Can equations always be solved using the Zero-Product Property?
4. How do you handle equations with more than two factors?
5. How can you verify the solutions of a factored equation?

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

Learn how to solve the factored equation (3w - 4)(6 + w) = 0 using the Zero-Product Property. This problem covers key algebraic concepts such as factored equations and how to set each factor equal to zero. Suitable for students in Grades 7-9.

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