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: $$x=0\text{and}x=\frac{3}{2}$$

So the final answers are: $$\boxed{{\displaystyle 0}}\text{and}\boxed{{\displaystyle \frac{3}{2}}}$$