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 $x$.