Given the equation is y = x² + 5x + 6.
Its x-intercepts would be the points (x,0) i.e. y=0. So we must plug y=0 into given equation and solve it for x.
y = x² + 5x + 6
0 = x² + 5x + 6
x² + 5x + 6 = 0
x² + 3x + 2x + 6 = 0
x(x + 3) + 2(x + 3) = 0
(x + 2)(x + 3) = 0
x + 2 = 0 and x + 3 = 0
x = -2 and x = -3
So, x-intercepts are (-3,0) and (-2,0).