Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$e^{- x} \left(x - 3\right) = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 3$$
Numerical solution$$x_{1} = 99.432316424891$$
$$x_{2} = 83.4917816149558$$
$$x_{3} = 43.9557499214057$$
$$x_{4} = 59.664342946604$$
$$x_{5} = 113.396350396671$$
$$x_{6} = 79.51136695866$$
$$x_{7} = 38.1905363866884$$
$$x_{8} = 30.9653321772927$$
$$x_{9} = 65.6052138551392$$
$$x_{10} = 115.392040334004$$
$$x_{11} = 93.4517230466241$$
$$x_{12} = 111.400841299949$$
$$x_{13} = 63.6232240789579$$
$$x_{14} = 117.387900375534$$
$$x_{15} = 105.415520933891$$
$$x_{16} = 69.5733090128955$$
$$x_{17} = 49.8119589630405$$
$$x_{18} = 77.5221246603965$$
$$x_{19} = 85.4828412467504$$
$$x_{20} = 61.642856145511$$
$$x_{21} = 101.426455152084$$
$$x_{22} = 75.5336138177003$$
$$x_{23} = 53.7430576092052$$
$$x_{24} = 40.0970717014418$$
$$x_{25} = 42.020216210141$$
$$x_{26} = 87.4744046501982$$
$$x_{27} = 119.383920620405$$
$$x_{28} = 109.405524706139$$
$$x_{29} = 89.466430197318$$
$$x_{30} = 3$$
$$x_{31} = 51.7754697845928$$
$$x_{32} = 97.4384664647568$$
$$x_{33} = 91.4588807455217$$
$$x_{34} = 71.5591096232555$$
$$x_{35} = 55.714063380457$$
$$x_{36} = 32.6626982028378$$
$$x_{37} = 103.420862702525$$
$$x_{38} = 57.6879649775293$$
$$x_{39} = 36.3071598061728$$
$$x_{40} = 67.5886304003902$$
$$x_{41} = 107.410413305772$$
$$x_{42} = 121.380091923383$$
$$x_{43} = 73.545912319012$$
$$x_{44} = 81.5012725708786$$
$$x_{45} = 47.853370487631$$
$$x_{46} = 34.4578471962376$$
$$x_{47} = 95.444927247289$$
$$x_{48} = 34.2046743865559$$
$$x_{49} = 45.9008089996782$$