To solve the quadratic equation \( x^2 + 3x + 2 = 0 \), we can use factoring, completing the square, or the quadratic formula. In this case, factoring is the simplest approach:

### Step 1: Factor the Equation
The equation is of the form \( ax^2 + bx + c = 0 \). Here, \( a = 1 \), \( b = 3 \), and \( c = 2 \). We look for two numbers that multiply to \( c \) (2) and add to \( b \) (3). These numbers are 1 and 2.

So, we can factor the equation as:

\[
x^2 + 3x + 2 = (x + 1)(x + 2) = 0
\]

### Step 2: Set Each Factor to Zero
Set each factor equal to zero:

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

### Step 3: Solve for \( x \)
Solving each equation:

1. \( x = -1 \)
2. \( x = -2 \)

### Final Solutions
The solutions to the equation are:

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

Would you like further details or explanations?

### Related Questions:
1. How would you solve \( x^2 - 5x + 6 = 0 \)?
2. Can you explain how the quadratic formula works?
3. What are the applications of quadratic equations in real life?
4. How do you complete the square for quadratic equations?
5. What happens if the quadratic equation cannot be factored easily?

### Tip:
Always check your factors by expanding them back to the original equation to ensure accuracy!

Learn how to solve the quadratic equation x^2 + 3x + 2 = 0 using factoring with a detailed step-by-step solution. This problem involves key algebraic concepts, including factoring quadratic equations and the quadratic formula. Suitable for students in Grades 7-9.

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