What are all the exact solutions of 2sin^2x-sinx=0 for 0

The exact solutions are:

Using zero product rule:

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x = {0, π/6}

Step-by-step explanation:

   2sin^2x-sinx=0

and i know the answer is this..

   2sin²(x) - sin(x) = 0

   sin2(x) is sin(x) × sin(x) so 2sin²(x) - sin(x) = 2 sin(x) × sin(x) - sin(x) and this expression has a common factor of sin(x) so

     2sin²(x) - sin(x) = 2 sin(x) × sin(x) - sin(x) = sin(x) [2 sin(x) - 1]

    sin(x)(2sin(x)-1) = 0

     sin(x) = 0

    x = 0

     2sin(x) - 1 = 0

    sin(x) = 1/2

    x = π/6

    x = {0, π/6}