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To determine the x-intercepts of the quadratic equation given as \( y = (2x - 3)(x - 6) \), we need to find the values of \( x \) that make \( y = 0 \).

### Step-by-Step Solution:
1. **Set the equation to zero**:
   \[
   (2x - 3)(x - 6) = 0
   \]

2. **Solve for each factor**:
   - For \( 2x - 3 = 0 \):
     \[
     2x - 3 = 0 \implies 2x = 3 \implies x = \frac{3}{2} = 1.5
     \]

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

3. **Find the x-intercepts**:
   The x-intercepts are the points where \( y = 0 \). Thus, the intercepts are:
   \[
   (1.5, 0) \quad \text{and} \quad (6, 0)
   \]

### Final Answer:
The correct choice is **Item 4**: \((1.5, 0)\) and \((6, 0)\).

Would you like more details or have any questions about this solution?

Here are 5 related questions that might help deepen your understanding:
1. How do you factor a quadratic equation to find its x-intercepts?
2. What are the key differences between standard form and factored form of a quadratic?
3. How can you verify x-intercepts by plugging them back into the original equation?
4. How do x-intercepts relate to the graph of a quadratic function?
5. What other methods can you use to find the x-intercepts of a quadratic equation?

**Tip:** For any quadratic equation in factored form, the x-intercepts can be found by setting each factor equal to zero and solving for \( x \).

What are the x-intercepts of the quadratic equation y = (2x - 3)(x - 6)?

Discover how to find the x-intercepts of the quadratic equation y = (2x - 3)(x - 6). This problem teaches key algebraic concepts, including factoring and the zero product property. Suitable for students in Grades 8-10.

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