Question 905763
{{{x^2abs(x-5)>6x}}}

{{{x^cross(2)abs(x-5)>6cross(x)}}}

{{{x*abs(x-5)>6 }}}same as {{{x+-sqrt((x-5)^2)>6}}}

so, we have

{{{x(x-5)>6 }}}or {{{x(-(x-5))>6}}}

if {{{x(x-5)>6}}}, than we have
{{{x^2-5x>6}}}
{{{x^2-5x-6>0}}}
{{{x^2+x-6x-6>0}}}write {{{5x}}} as {{{-x+6x}}}}
{{{(x^2+x)-(6x+6)>0}}}...group
{{{x(x+1)-6(x+1)>0}}}

{{{(x+1)(x-6)>0}}}

solutions:
if {{{(x+1) >0}}} => {{{x>-1}}}
if  {{{(x-6)>0}}}=> {{{x>6}}}

if {{{x(-(x-5))>6}}}, than we have

{{{x(-x+5)>6}}}
{{{-x^2+5x>6}}}
{{{-x^2+5x-6>0}}}....write {{{5x}}} as {{{2x+3x}}}}
{{{-x^2+2x+3x-6>0}}}...group
{{{-(x^2-2x)+(3x-6)>0}}}
{{{-x(x-2)+3(x-2)>0}}}
{{{(x-2)(3-x)>0}}}
if {{{(x-2)>0}}} => {{{x>2}}}
if {{{(3-x)>0}}}=> {{{3>x}}} or {{{x<3}}}
solution
{{{2<x<3}}}

so, your solutions are:

{{{x>-1}}}
{{{2<x<3}}}
{{{x>6}}}