Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
The quadratic equation is: 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 that fit this criteria are 2 and 3.
Therefore, the factored form of the equation is: (x + 2)(x + 3) = 0
Setting each factor to zero and solving for x, we get:
x + 2 = 0 or x + 3 = 0
x = -2 or x = -3
So the solutions to the quadratic equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.