Question 983632


Let us introduce a new variable.


Let &nbsp;<B>y</B>&nbsp; be &nbsp;{{{2^x}}}: &nbsp;&nbsp;{{{y}}} = {{{2^x}}}. 


Then you can re-write your equation in the form


{{{2y^3}}} - {{{3y}}} + {{{2y}}} = {{{y}}}.


Collect common terms:


{{{2y^3}}} = {{{2y}}}.


Since &nbsp;{{{y}}} = {{{2^x}}}&nbsp; can not be zero, &nbsp;you can divide both sides by &nbsp;{{{2y}}}, &nbsp;and you will get 


{{{y^2}}} = {{{1}}}.


It implies &nbsp;{{{y}}} = {{{1}}}.


Hence, &nbsp;{{{2^x}}} = {{{1}}}. 


Therefore, &nbsp;x = 0. 


<B>Answer</B>. &nbsp;x = 0.