x^2+3x+2=0

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

We need to find two numbers that multiply to \(2\) (the constant term) and add to \(3\) (the coefficient of the linear term). The numbers \(1\) and \(2\) satisfy these conditions since:

• \(1 \times 2 = 2\)
• \(1 + 2 = 3\)

Thus, we can factor the equation as:

\[ (x + 1)(x + 2) = 0 \]

Now, we can set each factor equal to zero:

1. \(x + 1 = 0\) → \(x = -1\)
2. \(x + 2 = 0\) → \(x = -2\)

Therefore, the solutions to the equation \(x^2 + 3x + 2 = 0\) are:

\[ x = -1 \quad \text{and} \quad x = -2 \]