You can put this solution on YOUR website! You can identify the zeros just by inspection. Test within each interval of the x-axis for sign within the intervals to know if y is positive or negative; and to help identify if y touches the x-axis.
You must do the work; but the graph should look like this:
(THIS GRAPH WILL NOT WORK. I WILL KEEP TRYING TO STRAIGHTEN THIS...)
Graph is still not working.
Try this: visit www.google.com, put y=-x(x+5)(x+3) into the search field, click the GO button, and you should be shown an interactive graph.