The first and the simplest approach to solve a quadratic equation is the splitting the middle term method. Not all quadratic equations can be solved by this method. When this method fails, the Quadratic Formula should be applied.
Here, we have
x^2 + 5x + 6 = 0
=> x^2 + 3x + 2x + 6 = 0
=> x(x + 3) + 2(x + 3) = 0
=> (x + 2)(x + 3) = 0
=> x = -2, x = -3
Hence, the solutions for x^2 + 5x + 6 = 0 are x = -2 and x = -3.
Here, we have
x^2 + 5x + 6 = 0
=> x^2 + 3x + 2x + 6 = 0
=> x(x + 3) + 2(x + 3) = 0
=> (x + 2)(x + 3) = 0
=> x = -2, x = -3
Hence, the solutions for x^2 + 5x + 6 = 0 are x = -2 and x = -3.
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