Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$e^{3 x} x = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
Numerical solution$$x_{1} = -32.9486642444431$$
$$x_{2} = -74.9005485194854$$
$$x_{3} = -86.895779213308$$
$$x_{4} = -36.9387450640686$$
$$x_{5} = -46.9220965396229$$
$$x_{6} = -38.9346459151651$$
$$x_{7} = -92.8938781666278$$
$$x_{8} = -94.8933003357084$$
$$x_{9} = -70.9025193770283$$
$$x_{10} = 0$$
$$x_{11} = -13.1416111389768$$
$$x_{12} = -24.98010213912$$
$$x_{13} = -21.0073010205309$$
$$x_{14} = -66.9047415605498$$
$$x_{15} = -17.0522033058526$$
$$x_{16} = -34.9433802056$$
$$x_{17} = -48.9196619333906$$
$$x_{18} = -19.0265962551348$$
$$x_{19} = -28.9618160346074$$
$$x_{20} = -106.890305626567$$
$$x_{21} = -98.8922178388967$$
$$x_{22} = -60.9086624652399$$
$$x_{23} = -88.8951156279565$$
$$x_{24} = -96.8927474190871$$
$$x_{25} = -68.9035961391333$$
$$x_{26} = -30.9547443398454$$
$$x_{27} = -42.9277215719632$$
$$x_{28} = -26.9701450522659$$
$$x_{29} = -76.8996443728558$$
$$x_{30} = -100.891710147796$$
$$x_{31} = -62.9072664632937$$
$$x_{32} = -15.0879331724686$$
$$x_{33} = -54.91351121676$$
$$x_{34} = -52.9153929935434$$
$$x_{35} = -72.9015052766187$$
$$x_{36} = -40.9309946683666$$
$$x_{37} = -50.9174360047675$$
$$x_{38} = -78.8987886111081$$
$$x_{39} = -56.9117722918857$$
$$x_{40} = -84.8964756651569$$
$$x_{41} = -64.9059624301828$$
$$x_{42} = -11.2328152835375$$
$$x_{43} = -80.8979774495789$$
$$x_{44} = -90.894482635299$$
$$x_{45} = -102.891223015744$$
$$x_{46} = -104.890755218345$$
$$x_{47} = -22.9922211573021$$
$$x_{48} = -58.9101605312548$$
$$x_{49} = -82.8972074884783$$
$$x_{50} = -44.9247706684296$$