To solve the equation \( 5x (x + 12) = 0 \) using the zero product property, we can set each factor of the equation equal to zero. The zero product property states that if the product of two factors is zero, at least one of the factors must be zero.
The factors in our equation are \( 5x \) and \( (x + 12) \).
-
Set the first factor equal to zero: \[ 5x = 0 \] Dividing both sides by 5 gives: \[ x = 0 \]
-
Set the second factor equal to zero: \[ x + 12 = 0 \] Subtracting 12 from both sides gives: \[ x = -12 \]
Thus, the solutions to the quadratic equation \( 5x (x + 12) = 0 \) are: \[ x = 0 \quad \text{and} \quad x = -12 \]