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I am trying to understand how to solve the equation

$$2\sin^2x + 3\sin x + 1 = 0.$$

Please give hints.

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Hi, welcome to math.SE! Can you show what you've done so far, and what you're having trouble with? We prefer to help you understand and solve things on your own, rather than being a homework-solving service. –  Jonathan Christensen Dec 20 '12 at 23:39
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Please avoid using "ASAP" when asking for help here. It's impolite. –  Asaf Karagila Dec 20 '12 at 23:39
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Nevermind, I just had to factor it into (sinx + 1)(2sinx + 1). –  Bilbo Dec 20 '12 at 23:42
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Have you thought of substituting $y=\sin x$? –  Mark Bennet Dec 20 '12 at 23:43
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@EricNaslund The edited version of this question does not only change the tone slightly, rather it contradicts explicit demands made by the OP in the original version, namely, to solve this for them and to show the steps, ASAP. One might view such a modification as problematic. –  Did Dec 20 '12 at 23:49
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2 Answers

Hint: Let $y=\sin x$. Solve for $y$ first, then solve for $x$.

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Just treat $\sin x$ as a variable, and solve the polynomial.

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