Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\frac{3 \left(1 - \frac{x - 1}{x}\right) \left(x - 1\right) \left(2 - \frac{4 \left(x - 1\right)}{x}\right)}{x^{3}} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 1$$
$$x_{2} = 2$$
Numerical solution$$x_{1} = -34271.1096332069$$
$$x_{2} = 36095.6746122884$$
$$x_{3} = -38508.302724897$$
$$x_{4} = 35248.2665114154$$
$$x_{5} = 29316.741005938$$
$$x_{6} = -30881.5128109348$$
$$x_{7} = 42875.2266561657$$
$$x_{8} = -36813.4033170219$$
$$x_{9} = 2$$
$$x_{10} = 21691.9449004357$$
$$x_{11} = -32576.2906256972$$
$$x_{12} = 30164.0590348464$$
$$x_{13} = 32706.105540728$$
$$x_{14} = -22408.5526344181$$
$$x_{15} = 18304.1905288149$$
$$x_{16} = -17326.1328949111$$
$$x_{17} = -19867.1489763855$$
$$x_{18} = -27492.1099957519$$
$$x_{19} = -24950.230650707$$
$$x_{20} = 31011.393343158$$
$$x_{21} = 19997.9475413141$$
$$x_{22} = -25797.5042085849$$
$$x_{23} = 33553.4811458175$$
$$x_{24} = -41050.6983637034$$
$$x_{25} = 41180.297877955$$
$$x_{26} = 22539.0157924593$$
$$x_{27} = 37790.5180779249$$
$$x_{28} = -39355.7621234367$$
$$x_{29} = -35118.5327803269$$
$$x_{30} = 36943.0920166792$$
$$x_{31} = 40332.8425767401$$
$$x_{32} = -33423.6953588215$$
$$x_{33} = 39485.3938707266$$
$$x_{34} = 27622.1600560727$$
$$x_{35} = 28469.4407751211$$
$$x_{36} = -20714.2471393572$$
$$x_{37} = 34400.8684267805$$
$$x_{38} = -31728.8961712578$$
$$x_{39} = 17457.4256853489$$
$$x_{40} = -21561.3830493695$$
$$x_{41} = 20844.9200706922$$
$$x_{42} = 31858.7425802053$$
$$x_{43} = -23255.7523879451$$
$$x_{44} = 42027.7593635588$$
$$x_{45} = -24102.9792739707$$
$$x_{46} = 25080.455758456$$
$$x_{47} = 38637.9522079391$$
$$x_{48} = 23386.1274629673$$
$$x_{49} = 25927.6651836085$$
$$x_{50} = -18173.0857508083$$
$$x_{51} = -29186.7830897556$$
$$x_{52} = -26644.7979196175$$
$$x_{53} = 24233.2754066656$$
$$x_{54} = 26774.9007897951$$
$$x_{55} = -19020.0933166933$$
$$x_{56} = -35965.9641926883$$
$$x_{57} = 19151.0347303634$$
$$x_{58} = -30034.1414487637$$
$$x_{59} = -28339.4388544017$$
$$x_{60} = -41898.1745189335$$
$$x_{61} = -40203.2274554761$$
$$x_{62} = -37660.8496483641$$