Write a quadratic equation that can be solved by factoring. Solve your equation and show all your work.

Quadratic equation:

x^2 + 5x + 6 = 0

To solve this equation by factoring, we need to find two numbers that multiply to 6 and add up to 5. The numbers are 2 and 3.

(x + 2)(x + 3) = 0

Setting each factor to zero:

x + 2 = 0 and x + 3 = 0

x = -2 and x = -3

Therefore, the solutions to the quadratic equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.