To solve the equation:

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

we apply the **zero-product property**, which states that if \( a \cdot b = 0 \), then \( a = 0 \) or \( b = 0 \).

So, we set each factor equal to zero:

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

### Solving for \( x \):
1. From \( x + 3 = 0 \):
   \[
   x = -3
   \]

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

### Solution
The solutions are:
\[
x = -3 \quad \text{or} \quad x = 6
\]

Would you like further details or have any questions about this process?

---

1. What does the zero-product property state, and how is it used?
2. How would you verify the solutions in this equation?
3. Can quadratic equations always be solved by factoring?
4. What if this equation was expanded to a standard quadratic form, \( ax^2 + bx + c = 0 \)?
5. How does this solution method compare to using the quadratic formula?

**Tip:** Always check if a quadratic can be factored before using other methods; it's often quicker!

Learn how to solve the factored quadratic equation (x + 3)(x - 6) = 0 using the zero-product property. This step-by-step guide demonstrates essential algebraic techniques in quadratic equations, suitable for students in Grades 8-10.

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