https://file.aiquickdraw.com/mathbot/file/1726802278054nkrf6qcp.jpg

The equation presented in the image is:

\[
y(y - 3)(y + 6) = 0
\]

To solve this equation, we can use the **zero-product property**, which states that if a product of factors equals zero, then at least one of the factors must be zero. The factors here are:

1. \( y = 0 \)
2. \( y - 3 = 0 \) → \( y = 3 \)
3. \( y + 6 = 0 \) → \( y = -6 \)

Thus, the solution set is:

\[
y = 0, 3, -6
\]

Would you like further details or explanation? Here are some follow-up questions:

1. How can the zero-product property help solve quadratic equations?
2. Why do we set each factor of the equation equal to zero?
3. How would you solve a quadratic equation without factoring?
4. What is the significance of having multiple solutions in such an equation?
5. Can the zero-product property apply to polynomials with more than two factors?

**Tip:** Always ensure that the equation is factored completely before applying the zero-product property.

Solve the following equation: y(y - 3)(y + 6) = 0

Learn how to solve the quadratic equation y(y - 3)(y + 6) = 0 using the zero-product property. This algebra problem involves factoring and determining the solutions to the equation, suitable for students in Grades 8-10.

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