x²+3x+2=0

To solve the quadratic equation \(x^2 + 3x + 2 = 0\), we can factor the equation.

1. Factoring: We look for two numbers that multiply to \(2\) (the constant term) and add up to \(3\) (the coefficient of \(x\)).

   The numbers \(1\) and \(2\) work because:

   • \(1 \times 2 = 2\)
   • \(1 + 2 = 3\)

   So we can factor the quadratic equation as: \[ (x + 1)(x + 2) = 0 \]

2. Setting each factor to zero: Now, we set each factor equal to zero: \[ x + 1 = 0 \quad \text{or} \quad x + 2 = 0 \]

   Solving these equations gives: \[ x = -1 \quad \text{or} \quad x = -2 \]

3. Solutions: The solutions to the equation \(x^2 + 3x + 2 = 0\) are: \[ x = -1 \quad \text{and} \quad x = -2 \]

Thus, the final answer is \(x = -1\) and \(x = -2\).