SOLUTION: Solve the equation 12sin^3x-20sin^2x+sinx+3=0 given that 2sinx-1 is one factor and x is in between 0 and 360 degrees.

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Question 1186338: Solve the equation 12sin^3x-20sin^2x+sinx+3=0 given that 2sinx-1 is one factor and x is in between 0 and 360 degrees.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let y = sinx.
===> The equation can be represented as 12y%5E3+-+20y%5E2+%2B+y+%2B3=0. From the hint, 2y - 1 is a factor of the left-hand side.

===> 6y%5E2+-+7y+-+3+=+0 after dividing both sides by 2y - 1.
===> (3y + 1)(2y - 3) = 0 ===> y = -1/3 or 3/2.

Since y = sinx = 3/2 has no solution, we solve y = sinx = -1/3.

===> x = red%28199.47%29, red%28340.53%29 (both in degrees).

Finally the solutions for 2sinx - 1 = 0, or sinx = 1/2, are x = red%2830%29, red%28150%29 (both in degrees).

All the values in red ink are the solutions to the original equation.