Solve the inequality x^3 + x^2 > 6x

Start by moving all the terms to one side of the inequality. In this case it's easiest to move the 6x to the left hand side by subtracting 6x from both sides, so that you are left with x^3 + x^2 - 6x > 0. Then factorise the cubic equation so that you get x(x+3)(x-2) > 0. From this form you can see that x=0 ; x= -3 and x= 2 solve the cubic equation, so these are the points, where the graph of y= x^3 + x^2 - 6x crosses the line y=0 (the x axis). Next sketch the cubic graph and you will be able to see clearly, which values solve the inequality. In this case, since x^3 + x^2 - 6x >0 it will be all the parts of the graph above the x axis, which are -3 < x < 0 and x > 2.