https://file.aiquickdraw.com/mathbot/file/1727055675682cz5i6scn.jpg

The given equation is:

\[
x(15 + 3x) = 0
\]

To solve this, we use the **zero product property**, which states that if the product of two factors equals zero, then at least one of the factors must be zero. The two factors here are \( x \) and \( (15 + 3x) \).

### Step-by-step solution:

1. First, set each factor equal to zero:
   \[
   x = 0
   \]
   and
   \[
   15 + 3x = 0
   \]

2. Solve \( 15 + 3x = 0 \):
   \[
   3x = -15
   \]
   \[
   x = \frac{-15}{3} = -5
   \]

### Solutions:
The two solutions are:
\[
x = 0 \quad \text{or} \quad x = -5
\]

### Correct Answer:
Based on the choices provided in the image, the correct option is **B. 0, -5**.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would the solution change if the equation were \( x(15 + 3x) = 7 \)?
2. Can this method be applied to equations with more complex factors, like \( x(x^2 + 3x + 2) = 0 \)?
3. What is the importance of the zero product property in solving quadratic equations?
4. How would you graph the equation \( x(15 + 3x) = 0 \), and what would the intercepts represent?
5. Could you factor the expression \( x(15 + 3x) \) further to see it in another form?

### Tip:
Always check each factor separately when solving factored equations, and don't forget to verify if they satisfy the original equation!

This page explains how to solve the algebraic equation x(15 + 3x) = 0 using the zero product property. Learn step-by-step how to break down the factors and find the solutions x = 0 and x = -5. Ideal for students in Grades 8-10.

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