x2+7x+12=0

Solution:

1. Given quadratic equation:
x^2 + 7x + 12 = 0

2. Factor the quadratic equation:
- Find two numbers that multiply to 12 (constant term) and add to 7 (coefficient of x.

3. These two numbers are 3 and 4 because:
3 \cdot 4 = 12
3 + 4 = 7

4. Write the equation in factored form:
(x + 3)(x + 4) = 0

5. Set each factor equal to zero:
x + 3 = 0 or x + 4 = 0

6. Solve for x:
x = -3 or x = -4

The solutions to the quadratic equation are x = -3 and x = -4.