Question

1. which are the solutions to the equation $2m (m - 4) (3m + 2) = 0$?

Explanation:

Step1: Apply Zero-Product Property

The Zero-Product Property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \) (or both). For the equation \( 2m(m - 4)(3m + 2)=0 \), we set each factor equal to zero.
First factor: \( 2m = 0 \)
Second factor: \( m - 4 = 0 \)
Third factor: \( 3m + 2 = 0 \)

Step2: Solve \( 2m = 0 \)

Divide both sides by 2: \( m=\frac{0}{2}=0 \)

Step3: Solve \( m - 4 = 0 \)

Add 4 to both sides: \( m = 4 \)

Step4: Solve \( 3m + 2 = 0 \)

Subtract 2 from both sides: \( 3m=-2 \)
Divide by 3: \( m =-\frac{2}{3} \)

Answer:

The solutions are \( m = 0 \), \( m = 4 \), and \( m =-\frac{2}{3} \)