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To solve the given equation \((x - 10)(x + 7) = 0\), we can use 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.

We set each factor to zero and solve for \(x\):

1. \(x - 10 = 0\)
   \[
   x = 10
   \]

2. \(x + 7 = 0\)
   \[
   x = -7
   \]

Therefore, the two solutions are:
\[
x = 10 \quad \text{and} \quad x = -7
\]

Would you like further details or have any questions?

Here are five related questions to extend your understanding:
1. What is the **zero-product property**, and how is it used in solving equations?
2. How would you solve a quadratic equation if it were not factored already?
3. How would the solutions change if the equation were \((x - 10)(x + 7) = 5\) instead of 0?
4. What type of graph would represent the equation \((x - 10)(x + 7) = 0\)?
5. Can you expand \((x - 10)(x + 7)\) into a standard quadratic form?

**Tip**: Always check your solutions by substituting them back into the original equation to verify their correctness.

Find the two solutions to the equation (x - 10)(x + 7) = 0

Learn how to solve the factored quadratic equation (x - 10)(x + 7) = 0 using the zero-product property. Step-by-step instructions and key algebraic concepts are provided. Suitable for Grades 7-9.

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