To find the x-intercepts of the quadratic equation \( y = (2x - 3)(x - 6) \), we need to set \( y \) to 0 and solve for \( x \):
\[ 0 = (2x - 3)(x - 6) \]
To find the x-intercepts, we set each factor equal to zero:
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Set \( 2x - 3 = 0 \): \[ 2x = 3 \ x = \frac{3}{2} \]
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Set \( x - 6 = 0 \): \[ x = 6 \]
Thus, the x-intercepts of the quadratic equation are:
\[ x = \frac{3}{2} \quad \text{and} \quad x = 6 \]
In coordinate form, the x-intercepts are \( \left(\frac{3}{2}, 0\right) \) and \( (6, 0) \).