intervals of increase and decrease

I need a bit of help here, I'm trying to figure out the intervals of increase and decrease, max and min points, intervals of concavity and any points of inflection for f(x)=x^3-x^2+4x-3, but I can't get through the increase and decrease intervals.

I know to find the intervals I have to find when the first derivative equals zero, but thats exactly where I'm stuck.

3x^2-2x+4=0; there's no common factor and I can't find a number for x that will make the equation equal 0.

help please?