Let y=-x3-3x-2. Make a table of x-y values from which you can plot the points on the graph. The scaling of the graph is going to change so you'll need several graphs or colour-coding scale changes on the same graph paper to distinguish between different scales.
Start with x=-1, then y=1+3-2=2 (positive); x=0, y=-2 (negative). The change from positive negative means there is a solution for x between -1 and 0. This is where the curve crosses the x axis.
Refine the table by listing values of x between -1 and 0 (you will need a calculator from now on):
x y
-0.9 1.429
-0.8 0.912
-0.7 0.443
-0.6 0.016 You can stop at this point because the sign changes.
-0.5 -0.375. The graph goes from positive to negative between x=-0.6 and x=-0.5, so refine the table further. So now you need values starting at -0.59.
x y
-0.60 0.016
-0.59 -0.024621. Stop here because there was a sign change from positive to negative.
A value between -0.60 and -0.59 is -0.595. y=-0.0002913 approx, which is a sign change. So you keep refining the table and changing the scale of the graph to get closer and closer to the solution. For example, the whole width of the graph can correspond to a range of x values of 0.1 (one tenth). Dividing this interval into 10 gives a resolution to one hundredth or one thousandth. The vertical range also has to be changed to allow a smaller range for y.
This is a graphical way of finding solutions.