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2sinxcosx+sinx=0 equation

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Numerical solution:

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The solution

You have entered [src] 
2*sin(x)*cos(x) + sin(x) = 0
sin⁡(x)+2sin⁡(x)cos⁡(x)=0\sin{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)} = 0
Simplify
The graph
0-80-60-40-2020406080-1001005-5
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
     -2*pi
x2 = -----
       3
x2=−2π3x_{2} = - \frac{2 \pi}{3} 
     2*pi
x3 = ----
      3
x3=2π3x_{3} = \frac{2 \pi}{3} 
x3 = 2*pi/3
Sum and product of roots [src] 
sum
  2*pi   2*pi
- ---- + ----
   3      3
−2π3+2π3- \frac{2 \pi}{3} + \frac{2 \pi}{3} 
=
0
00 
product
  -2*pi 2*pi
0*-----*----
    3    3
2π3⋅0(−2π3)\frac{2 \pi}{3} \cdot 0 \left(- \frac{2 \pi}{3}\right) 
=
0
00 
0
Numerical answer [src] 
x1 = 65.9734457253857
x2 = -5612.97887441376
x3 = -79.5870138909414
x4 = -21.9911485751286
x5 = 21.9911485751286
x6 = -85.870199198121
x7 = -15.707963267949
x8 = -4.18879020478639
x9 = 73.3038285837618
x10 = -67.0206432765823
x11 = -35.6047167406843
x12 = 6.28318530717959
x13 = 2.0943951023932
x14 = 39.7935069454707
x15 = -39.7935069454707
x16 = -77.4926187885482
x17 = 28.2743338823081
x18 = 29.3215314335047
x19 = -94.2477796076938
x20 = -12.5663706143592
x21 = -73.3038285837618
x22 = -96.342174710087
x23 = 85.870199198121
x24 = -25.1327412287183
x25 = -53.4070751110265
x26 = 98.4365698124802
x27 = 20.943951023932
x28 = -90.0589894029074
x29 = -41.8879020478639
x30 = 64.9262481741891
x31 = 59.6902604182061
x32 = -23.0383461263252
x33 = 90.0589894029074
x34 = 56.5486677646163
x35 = -2.0943951023932
x36 = 41.8879020478639
x37 = 72.2566310325652
x38 = -50.2654824574367
x39 = 14.6607657167524
x40 = 79.5870138909414
x41 = 78.5398163397448
x42 = -87.9645943005142
x43 = 37.6991118430775
x44 = -6.28318530717959
x45 = -37.6991118430775
x46 = -43.9822971502571
x47 = -14.6607657167524
x48 = -100.530964914873
x49 = 8.37758040957278
x50 = -72.2566310325652
x51 = 52.3598775598299
x52 = -81.6814089933346
x53 = -46.0766922526503
x54 = -58.6430628670095
x55 = -33.5103216382911
x56 = -65.9734457253857
x57 = 0.0
x58 = 35.6047167406843
x59 = -28.2743338823081
x60 = -56.5486677646163
x61 = 96.342174710087
x62 = 31.4159265358979
x63 = 43.9822971502571
x64 = -83.7758040957278
x65 = 100.530964914873
x66 = 81.6814089933346
x67 = -75.398223686155
x68 = -8.37758040957278
x69 = 50.2654824574367
x70 = 48.1710873550435
x71 = 94.2477796076938
x72 = 4.18879020478639
x73 = 83.7758040957278
x74 = -59.6902604182061
x75 = 58.6430628670095
x76 = 12.5663706143592
x77 = -69.1150383789755
x78 = 54.4542726622231
x79 = 18.8495559215388
x80 = 34.5575191894877
x81 = 92.1533845053006
x82 = -48.1710873550435
x83 = 46.0766922526503
x84 = -29.3215314335047
x85 = 15.707963267949
x86 = 10.471975511966
x87 = 87.9645943005142
x88 = -9.42477796076938
x89 = -92.1533845053006
x90 = -52.3598775598299
x91 = 62.8318530717959
x92 = -31.4159265358979
x93 = 75.398223686155
x93 = 75.398223686155
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