Solve the following quadratic equation:
`(3x-5)(2x+3)=0`

Options

A. `x=5andx=-3`
B. `x=(5)/(3)andx=(3)/(2)`
C. `x=(5)/(3)andx=(-3)/(2)`
D. none of these

Explanation

To solve the quadratic equation \((3x-5)(2x+3)=0\), we will use the property that if the product of two factors is zero, then at least one of the factors must be zero.

### Step-by-Step Solution:

1. **Set Each Factor to Zero**:
We start with the equation:
\[ (3x - 5)(2x + 3) = 0 \]
This gives us two separate equations to solve:
\[ 3x - 5 = 0 \quad \text{or} \quad 2x + 3 = 0 \]

2. **Solve the First Equation**:
For the first equation \(3x - 5 = 0\):
\[ 3x = 5 \]
Now, divide both sides by 3:
\[ x = \frac{5}{3} \]

3. **Solve the Second Equation**:
For the second equation \(2x + 3 = 0\):
\[ 2x = -3 \]
Now, divide both sides by 2:
\[ x = -\frac{3}{2} \]

4. **Conclusion**:
The solutions to the quadratic equation \((3x-5)(2x+3)=0\) are:
\[ x = \frac{5}{3} \quad \text{and} \quad x = -\frac{3}{2} \]

### Final Answer:
The roots of the quadratic equation are:
\[ x = \frac{5}{3}, \quad x = -\frac{3}{2} \]