X Squared +5x+6=0 is quadratic equation in x. There are two roots of the equation.

x2 + 5x + 6 = 0

x2 + 2x + 3x + 6 = 0 [5x splits into 2x and 3x]

x(x + 2) + 3(x + 2) = 0 [taking common x from first two terms and 3 from third and fourth term]

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

x + 2 = 0; x + 3 = 0 [ if ab=0, then either a= 0 or b=0]

x = -2; x = -3

x = -2, -3

So, the values of x are -2 and -3 respectively.

x2 + 5x + 6 = 0

x2 + 2x + 3x + 6 = 0 [5x splits into 2x and 3x]

x(x + 2) + 3(x + 2) = 0 [taking common x from first two terms and 3 from third and fourth term]

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

x + 2 = 0; x + 3 = 0 [ if ab=0, then either a= 0 or b=0]

x = -2; x = -3

x = -2, -3

So, the values of x are -2 and -3 respectively.