Solve `2sin^2x+5sinx-3=0` for `0<=x<=2pi` :

`2sin^2x+5sinx-3=0`

`(2sinx-1)(sinx+3)=0`

`sinx+3=0 ==>sinx=-3` but the range of sinx is `-1<=y<=1`

`2sinx-1=0==>sinx=1/2`

The sin is equal to 1/2 at `pi/6 +k2pi,(5pi)/6+k2pi` where k is an integer.

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**For `0<=x<=2pi` we have `x=pi/6,(5pi)/6` **

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The graph: