Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$e^{2 x} x = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
Numerical solution$$x_{1} = -62.4594813057761$$
$$x_{2} = -22.6957023751319$$
$$x_{3} = -96.4242823853152$$
$$x_{4} = -48.4905367883253$$
$$x_{5} = -74.443042965628$$
$$x_{6} = -58.4666463153532$$
$$x_{7} = -88.4299412042358$$
$$x_{8} = -108.417456216542$$
$$x_{9} = -44.5036237757639$$
$$x_{10} = -60.4629310925067$$
$$x_{11} = -98.4230212294978$$
$$x_{12} = -100.421813657552$$
$$x_{13} = -104.419546152707$$
$$x_{14} = -66.4532716391802$$
$$x_{15} = -18.8120890441258$$
$$x_{16} = -84.4332052360421$$
$$x_{17} = -15.0740840979127$$
$$x_{18} = -28.6042039159275$$
$$x_{19} = -78.4387803330419$$
$$x_{20} = -80.4368216405647$$
$$x_{21} = -76.4408508191288$$
$$x_{22} = -64.4562694336153$$
$$x_{23} = -30.5841669729212$$
$$x_{24} = -54.4750062227357$$
$$x_{25} = -92.4269803908933$$
$$x_{26} = -20.7448218335939$$
$$x_{27} = -56.4706589232168$$
$$x_{28} = -72.4453678375428$$
$$x_{29} = -16.9108476139709$$
$$x_{30} = -40.5198064107757$$
$$x_{31} = -70.4478378859715$$
$$x_{32} = -82.434965914994$$
$$x_{33} = -90.4284256014174$$
$$x_{34} = -68.4504671725702$$
$$x_{35} = 0$$
$$x_{36} = -94.4256007756744$$
$$x_{37} = -52.479732054378$$
$$x_{38} = -34.5528319076254$$
$$x_{39} = -38.5294259176999$$
$$x_{40} = -24.6581187031698$$
$$x_{41} = -110.416471439679$$
$$x_{42} = -42.5112629711588$$
$$x_{43} = -46.4967518857691$$
$$x_{44} = -102.420656323043$$
$$x_{45} = -26.628369572651$$
$$x_{46} = -106.418480319111$$
$$x_{47} = -36.5403401551302$$
$$x_{48} = -50.4848882937228$$
$$x_{49} = -32.567273706796$$
$$x_{50} = -86.4315324762772$$