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The given equation is:

\[
x(x + 10) = 0
\]

To find the two solutions, we apply the **zero product property**, which states that if a product of two factors equals zero, at least one of the factors must be zero. So we set each factor equal to zero:

1. \( x = 0 \)

2. \( x + 10 = 0 \), which simplifies to \( x = -10 \)

Thus, the two solutions are:

\[
x = 0 \quad \text{and} \quad x = -10
\]

Would you like more details or have any further questions?

Here are some related questions:
1. How do you solve quadratic equations like \( ax^2 + bx + c = 0 \)?
2. What is the zero product property, and when can it be used?
3. Can equations like \( (x + a)(x + b) = 0 \) have complex solutions?
4. How does factoring help in solving quadratic equations?
5. What is the geometric interpretation of the solutions to \( x(x + 10) = 0 \)?

**Tip:** Always check both solutions in the original equation to confirm their correctness!

Find the two solutions to the following equation: x(x + 10) = 0

Learn how to solve the equation x(x + 10) = 0 using factoring and the zero product property. This problem covers key algebraic concepts and is suitable for students in Grades 7-9.

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