Question 4387
First set the equation equal to zero, by subtracting {{{6x^2}}} from each side of the equation.

{{{3x^4 = 6 x^2}}}
{{{3x^4 - 6x^2 = 6 x^2- 6x^2}}}
{{{3x^4 - 6 x^2 = 0}}}

Factor the common factor of {{{3x^2}}} from the left side of the equation:
{{{3x^2 (x^2 - 2)=0}}}


Set each factor equal to zero:
{{{3x^2 = 0}}} or {{{x^2 - 2 = 0}}}


Now this is a technicality, but the only solution you can obtain strictly by factoring is from the first equation, x=0.  The second equation can be solved but not by factoring.  The second equation also gives real solutions, so you probably want those also, right?


{{{x^2 - 2=0}}}
{{{x^2 = 2}}}

{{{x = sqrt (2)}}} or {{{x=-sqrt (2)}}}


The final answer is {{{x=0}}}, {{{ x=sqrt(2)}}}, {{{x=-sqrt (2)}}}


R^2 at SCC