For this, we have to draw the graph first. As
x^2+3x+2=x^2+2xx3/2xx x+(3/2)^2+2-9/4=(x+3/2)^2-1/4
As (x+3/2)^2 is positive and its minimum value is zero, minimum value of x^2+3x+2 is -1/4, at x=-3/2.
Let y=x^2+3x+2 and we have a minimum at (-3/2,-1/4), some other points, we have by putting various values of x (around x=-3/2), are
(-5,12), (-4,6), (-3,2), (-2,0), (-1,0), (0,2), (1,6), (2,12) and joining all these eight points and the minimum at (-3/2,-1/4), we get following graph.
graph{x^2+3x+2 [-4.333, 0.667, -0.43, 2.07]}
As the value of y=0 at x=-1 and x=-2,
the solution is x=-1 and x=-2.
