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$$x_{1} = -99.1205993527235$$
$$x_{2} = -45.5740005056864$$
$$x_{3} = -111.089608132217$$
$$x_{4} = -95.1329980618501$$
$$x_{5} = -101.114833112977$$
$$x_{6} = -35.9540517145623$$
$$x_{7} = -113.085180982879$$
$$x_{8} = -47.5287883412543$$
$$x_{9} = -117.076847342498$$
$$x_{10} = -79.1981473783759$$
$$x_{11} = -115.080930865701$$
$$x_{12} = -59.3470343910748$$
$$x_{13} = -119.072920781941$$
$$x_{14} = -32.2742313644863$$
$$x_{15} = -107.099039845199$$
$$x_{16} = -69.2586229734047$$
$$x_{17} = -71.2447823410302$$
$$x_{18} = -73.2319064024203$$
$$x_{19} = -41.6870583075465$$
$$x_{20} = -89.1541152286569$$
$$x_{21} = -37.8463765939876$$
$$x_{22} = -85.1702113647074$$
$$x_{23} = -53.4230249783974$$
$$x_{24} = -83.1789726997072$$
$$x_{25} = -105.10407015753$$
$$x_{26} = -97.1266472537626$$
$$x_{27} = -51.4541901054407$$
$$x_{28} = -109.094223645316$$
$$x_{29} = -93.1396752246407$$
$$x_{30} = -87.1619388762717$$
$$x_{31} = -65.2896724119287$$
$$x_{32} = -34.0913241206348$$
$$x_{33} = -43.6261544568938$$
$$x_{34} = -63.3071694941258$$
$$x_{35} = -103.109329237227$$
$$x_{36} = -49.4891864944529$$
$$x_{37} = -39.7592416454249$$
$$x_{38} = -81.1882678183563$$
$$x_{39} = -91.146704685936$$
$$x_{40} = -67.2735421114241$$
$$x_{41} = -121.06914228288$$
$$x_{42} = -61.3262172000187$$
$$x_{43} = -55.3950840173982$$
$$x_{44} = -57.369883839131$$
$$x_{45} = -75.2198969347223$$
$$x_{46} = -2$$
$$x_{47} = -77.2086687051389$$