How would i work this problem out

we have the function f(x)=2x^3-3x^2-12x+20

first we have to find the zeroes. we cant use a calculator on this problem so i was thinking about using the anti derivative or something but you would need a point. any ideas?

also we need to write an equation for the line normal to the graph of f at x=0. I know the first step is to take the derivative of the equation and plug in the 0 but i forget if that solves for the tangent or normal slope.

lastly we need to find the x and y coordinates of all the points on the graph of f where the line tangent to the graph is parallel to the x-axis. Im not sure how to aproach that at all.