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I am having a problem solving the following equation. Please help.

$12(\cos(x))^3+2\cos(x)^2+(24\sin(x)-3)\cos(x)+2\sin(x)= 0$

Thank you in advance

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    What does this have to do with calculus? Also, what have you tried already?2012-10-29
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    Well I don't really know where to start..2012-10-29
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    Have you tried factoring by grouping?2012-10-29
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    What does that mean ?2012-10-29
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    Do you want a method or a result or both?2012-10-29
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    Method and a result please2012-10-29
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    just try using a couple of trigonometric identities for $cos^2 x$ or $sin x.cosx$ and see2012-10-29
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    So apparently, it isn't possible to determine exact values of x...2012-10-29
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    It might be worth checking the problem again (make sure you've transcribed it correctly) if this is an assigned problem, given the results provided by Robert below! Confirmed on WolframAlpha (it's not "pretty") in terms of solutions!2012-10-29

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$s = \sin(x)$ must satisfy the equation $144\,{s}^{6}-576\,{s}^{5}+220\,{s}^{4}+1000\,{s}^{3}-283\,{s}^{2}-424 \,s-77 = 0$. This has Galois group $S_6$, so it can't be solved in terms of radicals. Thus you aren't going to get nice closed-form solutions. The four solutions for $0 \le x \le 2 \pi$ are approximately $1.66661701719437, 3.42548142597468, 4.63849563287631, 5.91793801389173$ (found by numerical methods).

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    Do you mean that I can't find exact solutions?2012-10-29
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    That's right, you can't.2012-10-29