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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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    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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    That's right, you can't.2012-10-29