Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin^{2}{\left(2 x + 3 \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = - \frac{3}{2}$$
$$x_{2} = - \frac{3}{2} + \frac{\pi}{2}$$
Numerical solution$$x_{1} = -64.3318529519991$$
$$x_{2} = 20.4911484645524$$
$$x_{3} = 72.3274273108169$$
$$x_{4} = 64.4734456188499$$
$$x_{5} = -23.4911486889389$$
$$x_{6} = 58.1902604731576$$
$$x_{7} = -94.1769831742407$$
$$x_{8} = 37.7699082889724$$
$$x_{9} = -34.4867229570468$$
$$x_{10} = 53.4778711326136$$
$$x_{11} = -6.21238886463505$$
$$x_{12} = -31.3451302949883$$
$$x_{13} = -89.464594417458$$
$$x_{14} = 36.1991118880098$$
$$x_{15} = -42.340704378769$$
$$x_{16} = 48.7654827270239$$
$$x_{17} = 73.8982237628936$$
$$x_{18} = 45.6238899091033$$
$$x_{19} = -53.3362788620348$$
$$x_{20} = 89.6061870489026$$
$$x_{21} = 88.0353905684316$$
$$x_{22} = -40.7699076747787$$
$$x_{23} = 15.7787597122709$$
$$x_{24} = -28.2035374417416$$
$$x_{25} = -1.50000011229917$$
$$x_{26} = -86.3230015256305$$
$$x_{27} = 95.8893723423514$$
$$x_{28} = -29.7743338628789$$
$$x_{29} = -67.4734458415332$$
$$x_{30} = 59.7610568654647$$
$$x_{31} = 70.7566312418352$$
$$x_{32} = 81.752205441742$$
$$x_{33} = -15.6371670074559$$
$$x_{34} = 0.0707961048006144$$
$$x_{35} = -59.6194641657212$$
$$x_{36} = 31.4867226097166$$
$$x_{37} = -95.7477796093333$$
$$x_{38} = 23.6327413380252$$
$$x_{39} = 100.601761129251$$
$$x_{40} = 44.0530933625745$$
$$x_{41} = 56.6194639846237$$
$$x_{42} = -78.4690200383061$$
$$x_{43} = -58.0486677198505$$
$$x_{44} = 78.6106125566237$$
$$x_{45} = -72.185834596546$$
$$x_{46} = -7.78318527986359$$
$$x_{47} = 4.78318549937173$$
$$x_{48} = 6.35398157189193$$
$$x_{49} = -36.0575191385333$$
$$x_{50} = -51.7654824454163$$
$$x_{51} = -87.8937975071267$$
$$x_{52} = -75.3274274453509$$
$$x_{53} = 94.3185758907642$$
$$x_{54} = 86.4645941962783$$
$$x_{55} = 51.9070751831885$$
$$x_{56} = -73.7566310275489$$
$$x_{57} = -37.6283155866601$$
$$x_{58} = -12.4955744275382$$
$$x_{59} = 34.6283154133407$$
$$x_{60} = 75.4690197217621$$
$$x_{61} = -804.176923076907$$
$$x_{62} = -80.0398163016198$$
$$x_{63} = 22.061944743021$$
$$x_{64} = 29.9159266032184$$
$$x_{65} = -20.349555805984$$
$$x_{66} = -34.4867227269966$$
$$x_{67} = -14.066370557611$$
$$x_{68} = -45.4822972653549$$
$$x_{69} = -94.1769832428847$$
$$x_{70} = 92.747779760753$$
$$x_{71} = -9.35398172661415$$
$$x_{72} = 95.8893725783361$$
$$x_{73} = -100.460168587817$$
$$x_{74} = 9.49557409387618$$
$$x_{75} = 12.6371668428837$$
$$x_{76} = 26.7743341947881$$
$$x_{77} = 28.3451301513849$$
$$x_{78} = -81.610612744639$$
$$x_{79} = 67.6150384794371$$
$$x_{80} = -75.3274274274989$$
$$x_{81} = 14.2079633037244$$
$$x_{82} = -97.3185759910612$$
$$x_{83} = 42.4822970416052$$
$$x_{84} = -50.1946860190459$$
$$x_{85} = -56.4778714943287$$
$$x_{86} = 80.1814090593883$$
$$x_{87} = 50.3362787310254$$
$$x_{88} = 66.0442419694003$$
$$x_{89} = 1.64159276630259$$
$$x_{90} = 7.92477802296118$$