Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$e^{x} \left(x - 2\right) = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 2$$
Numerical solution$$x_{1} = -35.7592416454249$$
$$x_{2} = -57.3262172000187$$
$$x_{3} = -53.369883839131$$
$$x_{4} = -39.6261544568938$$
$$x_{5} = -69.2319064024203$$
$$x_{6} = -87.146704685936$$
$$x_{7} = -109.085180982879$$
$$x_{8} = -79.1789726997072$$
$$x_{9} = -71.2198969347223$$
$$x_{10} = -37.6870583075465$$
$$x_{11} = -45.4891864944529$$
$$x_{12} = -117.06914228288$$
$$x_{13} = -113.076847342498$$
$$x_{14} = -75.1981473783759$$
$$x_{15} = -101.10407015753$$
$$x_{16} = -49.4230249783974$$
$$x_{17} = 2$$
$$x_{18} = -61.2896724119287$$
$$x_{19} = -103.099039845199$$
$$x_{20} = -33.8463765939876$$
$$x_{21} = -67.2447823410302$$
$$x_{22} = -41.5740005056864$$
$$x_{23} = -47.4541901054407$$
$$x_{24} = -111.080930865701$$
$$x_{25} = -119.065503606275$$
$$x_{26} = -105.094223645316$$
$$x_{27} = -77.1882678183563$$
$$x_{28} = -107.089608132217$$
$$x_{29} = -85.1541152286569$$
$$x_{30} = -43.5287883412543$$
$$x_{31} = -121.06199711462$$
$$x_{32} = -51.3950840173982$$
$$x_{33} = -63.2735421114241$$
$$x_{34} = -97.1148331129772$$
$$x_{35} = -95.1205993527235$$
$$x_{36} = -55.3470343910748$$
$$x_{37} = -91.1329980618501$$
$$x_{38} = -93.1266472537626$$
$$x_{39} = -99.1093292372273$$
$$x_{40} = -81.1702113647074$$
$$x_{41} = -115.072920781941$$
$$x_{42} = -59.3071694941258$$
$$x_{43} = -73.2086687051389$$
$$x_{44} = -65.2586229734047$$
$$x_{45} = -83.1619388762717$$
$$x_{46} = -89.1396752246407$$
$$x_{47} = -31.9540517145623$$