To solve the equation \( x(x - 15) = 0 \) using the zero product property, we start by recognizing that this property states that if the product of two factors equals zero, then at least one of the factors must be equal to zero.
In our equation, we have two factors:
- \( x \)
- \( x - 15 \)
We can set each factor equal to zero and solve for \( x \).
Step 1: Set the first factor equal to zero. \[ x = 0 \]
Step 2: Set the second factor equal to zero. \[ x - 15 = 0 \]
To solve for \( x \), we add 15 to both sides: \[ x = 15 \]
Conclusion: The solutions to the equation \( x(x - 15) = 0 \) are: \[ x = 0 \quad \text{and} \quad x = 15 \]
Thus, the two solutions are \( x = 0 \) and \( x = 15 \).