(x-3)(x+12)(x+15)=0

To solve the equation \((x - 3)(x + 12)(x + 15) = 0\), we need to set each factor equal to zero.

1. Set \(x - 3 = 0\): \[ x = 3 \]

2. Set \(x + 12 = 0\): \[ x = -12 \]

3. Set \(x + 15 = 0\): \[ x = -15 \]

Therefore, the solutions to the equation \((x - 3)(x + 12)(x + 15) = 0\) are: \[ x = 3, \quad x = -12, \quad x = -15 \]