Question 163907
{{{3^(2x+1)+(28*3^(x))+9=0}}}

<=> {{{3^(2x)*3^(1) + 28*3^x + 9 = 0}}}
<=> {{{3*3^(2x) + 28*3^x + 9 = 0}}}

let {{{3^x = a}}}, then
{{{3*a^2 + 28*a + 9 = 0}}}

factorize this problem into this:
{{{(3a + 1)*(a + 9) = 0}}}

then we get:
3a + 1 = 0
<=> 3a = -1
<=> a = -1/3
change the variable a back to {{{3^x}}}
<=> {{{3^x = -1/3}}}
-> there is no answer for this equation

and try the other one:
a + 9 = 0
<=>a = -9
change the variable a back to {{{3^x}}}
<=> {{{3^x}}} = -9 
-> there is no answer for this equation too

so this equation problem has no solution