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 can follow these steps:

### Step 1: Set each factor to zero
Since the product of two factors equals zero, we can set each factor equal to zero:
\[ 3x - 5 = 0 \quad \text{or} \quad 2x + 3 = 0 \]

### Step 2: Solve the first equation
Now, let's solve the first equation:
\[ 3x - 5 = 0 \]
Add 5 to both sides:
\[ 3x = 5 \]
Now, divide both sides by 3:
\[ x = \frac{5}{3} \]

### Step 3: Solve the second equation
Next, we solve the second equation:
\[ 2x + 3 = 0 \]
Subtract 3 from both sides:
\[ 2x = -3 \]
Now, divide both sides by 2:
\[ x = -\frac{3}{2} \]

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

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