Question 882989
You are looking for values of the quadratic function, LESS than zero.  Think about this visually, like as a graph.  The expression is a parabola opening upward, so the vertex is a minimum.  The roots will be at y=0 and the vertex will be below the x-axis.  


You can factor the left side expression, so finding the roots is simple to do.
{{{x^2+x-6=(x-2)(x+3)<0}}}
Which tells you that the roots or zeros are at x=2 and x=-3.
<b>The solution is not -3 !</b>


You know you have a parabola opening upward with a minimum BETWEEN x=-3 and x=2.

LOOK at a graph of just the parabola function:
{{{graph(300,300,-10,10,-10,10,x^2+x-6)}}}


The function or expression will be LESS THAN ZERO for x between -3 and positive 2.


SOLUTION:  {{{highlight(highlight(-3<x<2))}}}.
You can also find the solution using the roots as critical points and testing any point in each interval which the critical points form.