https://file.aiquickdraw.com/mathbot/file/1727055177850hvdq0l2v.jpg

The equation shown in the image is:

\[
t(t + 9) = 0
\]

To solve this equation, we can 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. The two factors in this equation are:

1. \( t = 0 \)
2. \( t + 9 = 0 \)

Let's solve each:

1. From \( t = 0 \), we have one solution: \( t = 0 \).
2. From \( t + 9 = 0 \), subtract 9 from both sides to get \( t = -9 \).

Thus, the solutions are:

\[
t = 0 \quad \text{or} \quad t = -9
\]

### Final answer:
The solution is \( t = 0, -9 \).

Would you like more details or further explanations?

Here are 5 related questions to expand your understanding:
1. How do you solve quadratic equations that are not factorable?
2. What is the Zero Product Property and how is it used in solving equations?
3. Can you graph the solutions of \( t(t+9) = 0 \) on a coordinate plane?
4. How would the equation change if there was a constant added to it?
5. How do you solve quadratic equations using the quadratic formula?

**Tip**: Always check if an equation can be factored before trying more complex methods like completing the square or using the quadratic formula.

Learn how to solve the quadratic equation t(t + 9) = 0 by applying the Zero Product Property. This tutorial provides a step-by-step explanation of finding the solutions t = 0 and t = -9, suitable for students in Grades 7-9.

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