https://file.aiquickdraw.com/mathbot/file/1726494328862bzqt73ve.jpg

The equation provided is:

\[
-3y(y - 4) = 0
\]

To solve this, let's proceed step by step.

### Step 1: Apply the Zero Product Property
The equation involves a product of two factors. According to the **Zero Product Property**, if the product of two terms is zero, then at least one of the terms must be zero.

\[
-3y = 0 \quad \text{or} \quad (y - 4) = 0
\]

### Step 2: Solve for \( y \)
1. From \( -3y = 0 \):
   \[
   y = 0
   \]
2. From \( y - 4 = 0 \):
   \[
   y = 4
   \]

### Final Answer
The solutions to the equation are:
\[
y = 0 \quad \text{or} \quad y = 4
\]

Let me know if you'd like any further explanation or details!

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Here are 5 related questions you might find helpful:
1. What is the Zero Product Property?
2. How would you solve \( y(y - 2) = 0 \)?
3. Can a quadratic equation have more than two solutions?
4. How can we apply factoring to solve quadratic equations?
5. What does it mean if the coefficient of \( y^2 \) is negative in a quadratic equation?

**Tip**: When solving quadratic equations, always check for opportunities to use factoring or the Zero Product Property to simplify the process.

Learn how to solve the algebraic equation -3y(y - 4) = 0 using the Zero Product Property. This problem breaks down the steps to find the solutions for y, suitable for Grades 7-9 students.

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