Question 717597
{{{x^6 - x^2 = 0}}}...factor out {{{x^2}}}

{{{x^2 (x^4 - 1)= 0}}}.....write {{{x^4 - 1}}} as {{{(x^2)^2 - 1^2}}}


{{{x^2 ((x^2)^2 - 1^2)= 0}}}...factor {{{(x^2)^2 - 1^2}}} as {{{(x^2 - 1)(x^2+ 1)}}}

{{{x^2 ((x^2 - 1)(x^2+ 1))= 0}}}...factor {{{(x^2 - 1)}}} as {{{(x - 1)(x+1)}}}


{{{x^2 (x - 1)(x+1)(x^2+ 1)= 0}}}

solutions:

if {{{x^2=0}}}.....=>...{{{x=0}}}

if {{{x-1=0}}}.....=>...{{{x=1}}}

if {{{x+1=0}}}.....=>...{{{x=-1}}}

if {{{x^2+ 1=0}}}.....=>...{{{x^2=-1}}}.....=>...{{{x=sqrt(-1)}}}...=>...{{{x=i}}} or {{{x=-i}}}