How can we solve the following equation:
$(x+2)(x+3)(x+5)(x+12) = 4x^2$
Is there a simple technique to solve this?
Solving a biquadratic equation
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$\begingroup$
polynomials
problem-solving
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1Seing as [WolframAlpha](http://www.wolframalpha.com/input/?i=(x%2B2)(x%2B3)(x%2B5)(x%2B12)+%3D+4x%5E2) can't get a nice form for the solutions (go to "real solutions" and press "exact forms"), the odds are there is no nice way to solve it. Some times, WA fails to see simplifications, though, so there is still a _possibility_ that this is solvable by hand without the general quartic formula, but I wouldn't count on it. – 2017-01-27
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0https://en.wikipedia.org/wiki/Quartic_function#General_formula_for_roots – 2017-01-27
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0This is a quartic equation and it can be solved with radicals (hoping you enjoy them). For the method, have a look at https://en.wikipedia.org/wiki/Quartic_function – 2017-01-27
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0The title is kind of misleading since that is not a biquadratic equation. Are you interested in integer solutions, real solutions, real and positive solutions, complex solutions or what? – 2017-01-27