Using the zero product property, solve (r−6)(2r−15)=0.

Answer 1

To solve the equation \((r − 6)(2r − 15) = 0\) using the zero product property, we set each factor equal to zero:

1. Set the first factor equal to zero: \[ r - 6 = 0 \] Adding 6 to both sides gives: \[ r = 6 \]

2. Set the second factor equal to zero: \[ 2r - 15 = 0 \] Adding 15 to both sides gives: \[ 2r = 15 \] Now, divide by 2: \[ r = \frac{15}{2} = 7.5 \]

Thus, the solutions are: \[ r = 6 \quad \text{and} \quad r = 7.5 \]