To solve the equation:

\[
(x + 3)(x - 6) = 0
\]

we apply 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. So we set each factor equal to zero:

1. \( x + 3 = 0 \)
2. \( x - 6 = 0 \)

### Solving each equation:

1. For \( x + 3 = 0 \):
   \[
   x = -3
   \]

2. For \( x - 6 = 0 \):
   \[
   x = 6
   \]

### Solution:
The solutions to the equation are:

\[
x = -3 \quad \text{or} \quad x = 6
\]

Would you like more details or have any questions?

---

1. What if the factors were not simple binomials, but instead contained higher powers?
2. How would this solution change if there was an extra term outside the parentheses?
3. Can we verify these solutions by substitution into the original equation?
4. What if the equation had more than two factors multiplied together?
5. How does the zero-product property work for non-real (complex) roots?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy it.

Learn how to solve the equation (x + 3)(x - 6) = 0 by applying the zero-product property. This solution provides a step-by-step breakdown suitable for students in Grades 7-9, covering essential algebraic techniques like factoring and using the zero-product property.

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