Question Number 81223 by ubaydulla last updated on 10/Feb/20
$${x}\left(\mathrm{3}^{{x}} +\mathrm{2}\right)=\mathrm{3}\left(\mathrm{1}−\mathrm{3}^{{x}} \right)−{x}^{\mathrm{2}} \\ $$
Answered by MJS last updated on 10/Feb/20
$$\mathrm{3}^{{x}} {x}+\mathrm{2}{x}−\mathrm{3}+\mathrm{3}^{{x}} \mathrm{3}+{x}^{\mathrm{2}} =\mathrm{0} \\ $$$$\left({x}+\mathrm{3}\right)\left(\mathrm{3}^{{x}} +{x}−\mathrm{1}\right)=\mathrm{0} \\ $$$${x}=−\mathrm{3} \\ $$$$\mathrm{3}^{{x}} +{x}−\mathrm{1}=\mathrm{0}\:\mathrm{has}\:\mathrm{no}\:\mathrm{other}\:\mathrm{zero}\:\mathrm{than}\:{x}=\mathrm{0} \\ $$