Question 1209412
<pre> 
{{{(3x - 27)^3 + (27x - 3)^3}}}{{{""=""}}}{{{(3x + 27x - 30)^3}}}
{{{(3(x - 9))^3 + (3(9x - 1))^3}}}{{{""=""}}}{{{(30x - 30)^3}}}
{{{(3(x - 9))^3 + (3(9x - 1))^3}}}{{{""=""}}}{{{30(x - 1)^3}}}
{{{27(x - 9)^3 + 27(9x - 1)^3}}}{{{""=""}}}{{{27000(x - 1)^3}}}
{{{(x - 9)^3 + (9x - 1)^3}}}{{{""=""}}}{{{1000(x - 1)^3}}}

Factor the left side as the sum of two cubes:

{{{((x-9)+(9x-1)^"")((x-9)^2-(x-9)(9x-1)+(9x-1)^2)}}}{{{""=""}}}{{{1000(x-1)^3}}}
{{{(10x-10^"")((x-9)^2-(x-9)(9x-1)+(9x-1)^2)}}}{{{""=""}}}{{{1000(x-1)^3}}}
{{{(10(x-1)^"")((x^2-18x+81)-(9x^2-82x+9)+(81x^2-18x+1)^"")}}}{{{""=""}}}{{{1000(x-1)^3}}}
{{{(10(x-1)^"")(x^2-18x+81-9x^2+82x-9+81x^2-18x+1)}}}{{{""=""}}}{{{1000(x-1^"")^3}}}
{{{(10(x-1)^"")(73x^2+46x+73)}}}{{{""=""}}}{{{1000(x-1^"")^3=0}}}
{{{(x-1^"")(73x^2+46x+73)}}}{{{""=""}}}{{{100(x-1^"")^3}}}
{{{(x-1^"")(73x^2+46x+73)-100(x-1^"")^3}}}{{{""=""}}}{{{0}}}
{{{(x-1^"")((73x^2+46x+73)^""-100(x-1^"")^2)}}}{{{""=""}}}{{{0}}}
{{{(x-1^"")(73x^2+46x+73-100(x^2-2x+1))}}}{{{""=""}}}{{{0}}}
{{{(x-1^"")(73x^2+46x+73-100x^2+200x-100)}}}{{{""=""}}}{{{0}}}
{{{(x-1^"")(-27x^2+246x-27)}}}{{{""=""}}}{{{0}}}
Divide both sides by -3, since the 2nd factor on the left
is divisible by -3
{{{(x-1^"")(9x^2-82x+9)}}}{{{""=""}}}{{{0}}}
{{{(x-1)(9x-1)(x-9)}}}{{{""=""}}}{{{0}}}
x-1=0; 9x-1=0  ; x-9=0
  x=1;   9x=1  ;   x=9
          x={{{1/9}}};

So the three solutions are {{{1}}}, {{{1/9}}}, and {{{9}}}.

Edwin</pre>