Question Number 140430 by ajfour last updated on 07/May/21
$$\left(\mathrm{1}+\mathrm{2}{x}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{4}} +{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$=\left\{\left({x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)\right. \\ $$$$\left.\:\:\:\:\:\:\:−{x}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{2}{x}\right)\left({x}+\mathrm{3}\right)\right\}^{\mathrm{2}} \\ $$$${Any}\:{good}\:{non}-{zero}\:{real}\:{solution} \\ $$$${to}\:{this}\:{equation}\:{in}\:{the}\:{exact}\:{form} \\ $$$${with}\:{the}\:{help}\:{of}\:{a}\:{calculator}, \\ $$$${perhaps}…\left({please}\:{help}\right) \\ $$