To solve the quadratic equation \((x-5)(x+6)=0\), we can apply the **Zero Product Property**, which states that if the product of two factors equals zero, at least one of the factors must be zero.

So, we set each factor equal to zero:

1. \(x - 5 = 0\)
   
   Solving for \(x\):
   \[
   x = 5
   \]

2. \(x + 6 = 0\)
   
   Solving for \(x\):
   \[
   x = -6
   \]

Thus, the solutions are:
\[
x = 5 \quad \text{or} \quad x = -6
\]

Would you like any additional details or explanations?

Here are some related questions for you to explore:
1. What is the general form of a quadratic equation?
2. How do you factor a quadratic equation like \(x^2 + bx + c = 0\)?
3. What is the Zero Product Property?
4. Can you apply the quadratic formula to solve this equation?
5. How do you check if the solutions are correct?

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

Learn how to solve the quadratic equation (x-5)(x+6)=0 by applying the Zero Product Property. This detailed step-by-step guide explains the key algebraic concepts, factored forms, and important theorems. Perfect for students in Grades 8-10 looking to strengthen their algebra skills.

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