Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(2 x + 3 \right)} = 0$$
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$$x_{1} = -32.9159265358979$$
$$x_{2} = -43.9115008234622$$
$$x_{3} = 53.4778714378214$$
$$x_{4} = 67.6150383789755$$
$$x_{5} = -15.6371669411541$$
$$x_{6} = 89.606186954104$$
$$x_{7} = 15.7787595947439$$
$$x_{8} = -67.4734457253857$$
$$x_{9} = -20.3495559215388$$
$$x_{10} = -29.7743338823081$$
$$x_{11} = 81.7522053201295$$
$$x_{12} = 37.7699081698724$$
$$x_{13} = 7.92477796076938$$
$$x_{14} = -95.7477796076938$$
$$x_{15} = 70.7566310325652$$
$$x_{16} = -58.0486677646163$$
$$x_{17} = -51.7654824574367$$
$$x_{18} = -37.6283155162826$$
$$x_{19} = 80.1814089933346$$
$$x_{20} = -94.1769832808989$$
$$x_{21} = -45.4822971502571$$
$$x_{22} = 78.6106126665397$$
$$x_{23} = -73.7566310325652$$
$$x_{24} = 20.4911485751286$$
$$x_{25} = -31.345130209103$$
$$x_{26} = 28.345130209103$$
$$x_{27} = -56.4778714378214$$
$$x_{28} = 58.1902604182061$$
$$x_{29} = 94.3185759344887$$
$$x_{30} = 92.7477796076938$$
$$x_{31} = -36.0575191894877$$
$$x_{32} = 51.9070751110265$$
$$x_{33} = -86.3230016469244$$
$$x_{34} = 100.601761241668$$
$$x_{35} = 86.4645943005142$$
$$x_{36} = -81.6106126665397$$
$$x_{37} = 73.898223686155$$
$$x_{38} = -23.4911485751286$$
$$x_{39} = -59.6194640914112$$
$$x_{40} = -7.78318530717959$$
$$x_{41} = 59.761056745001$$
$$x_{42} = -6.21238898038469$$
$$x_{43} = 44.053093477052$$
$$x_{44} = 1.64159265358979$$
$$x_{45} = -100.460168588078$$
$$x_{46} = -28.2035375555132$$
$$x_{47} = -53.3362787842316$$
$$x_{48} = 0.0707963267948966$$
$$x_{49} = 22.0619449019235$$
$$x_{50} = -34.4867228626928$$
$$x_{51} = 23.6327412287183$$
$$x_{52} = -80.0398163397448$$
$$x_{53} = 50.3362787842316$$
$$x_{54} = -12.4955742875643$$
$$x_{55} = -9.35398163397448$$
$$x_{56} = -21.9203522483337$$
$$x_{57} = -50.1946861306418$$
$$x_{58} = 66.0442420521806$$
$$x_{59} = 45.6238898038469$$
$$x_{60} = 9.49557428756428$$
$$x_{61} = -75.3274273593601$$
$$x_{62} = -87.8937979737193$$
$$x_{63} = 31.4867228626928$$
$$x_{64} = -89.4645943005142$$
$$x_{65} = 95.8893722612836$$
$$x_{66} = 34.6283155162826$$
$$x_{67} = 64.4734457253857$$
$$x_{68} = -72.1858347057703$$
$$x_{69} = 88.0353906273091$$
$$x_{70} = 29.9159265358979$$
$$x_{71} = -78.4690200129499$$
$$x_{72} = 36.1991118430775$$
$$x_{73} = 12.6371669411541$$
$$x_{74} = -1.5$$
$$x_{75} = 42.4822971502571$$
$$x_{76} = 14.207963267949$$
$$x_{77} = 6.35398163397448$$
$$x_{78} = -65.9026493985908$$
$$x_{79} = -64.3318530717959$$
$$x_{80} = 56.6194640914112$$
$$x_{81} = -42.3407044966673$$
$$x_{82} = -97.3185759344887$$
$$x_{83} = 48.7654824574367$$
$$x_{84} = 72.3274273593601$$
$$x_{85} = -14.0663706143592$$