Solve 3x (2x - 3) = 0 using the zero product property. Leave answers as simplified fractions as necessary

Answer 1

To solve the equation \( 3x(2x - 3) = 0 \) using the zero product property, we can set each factor equal to zero.

The equation can be factored as two separate parts:

1. \( 3x = 0 \)
2. \( 2x - 3 = 0 \)

Now, we solve each equation separately.

For the first factor: \[ 3x = 0 \] Divide both sides by 3: \[ x = 0 \]

For the second factor: \[ 2x - 3 = 0 \] Add 3 to both sides: \[ 2x = 3 \] Now, divide both sides by 2: \[ x = \frac{3}{2} \]

Thus, the solutions for the equation \( 3x(2x - 3) = 0 \) are: \[ x = 0 \quad \text{and} \quad x = \frac{3}{2} \]

So the final answers are: \[ \boxed{0} \quad \text{and} \quad \boxed{\frac{3}{2}} \]