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The solutions are \( x=-5 \) and \( x=4.5 \).
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The Deep Dive
To solve the equation \( (2x-9)(3x+15)=0 \), we need to set each factor equal to zero. First, set \( 2x - 9 = 0 \): Add 9 to both sides: \[ 2x = 9 \] Now, divide by 2: \[ x = \frac{9}{2} \] or \( x = 4.5 \). Next, set \( 3x + 15 = 0 \): Subtract 15 from both sides: \[ 3x = -15 \] Now, divide by 3: \[ x = -5 \]. So the solutions are \( x = 4.5 \) and \( x = -5 \).
