Question 742642
"{{{ 3t^2 + 2 = 9t^4 }}}"

"My working:
{{{ (3t^2 + 1)(3t^2 - 2) = 0 }}}"


,..but you do not have a source for the difference of two squares.


{{{3t^2 + 2 = 9t^4}}}
{{{9t^4-3t^2-2=0}}}
Treating {{{t^2}}} as the variable and resorting to solution to quadratic formula,
you find {{{t^2=-1/3}}} or {{{t^2=2/3}}}.



No REAL solution from {{{t^2=-1/3}}}, but for the other intermediary result, {{{highlight(t=-sqrt(2/3))}}} or {{{highlight(t=sqrt(2/3))}}}.


One last detail to finish you may want is to rationalize the denominator.
{{{highlight((sqrt(2/3))*(sqrt(3)/sqrt(3))=sqrt(6)/3)}}}
and similarly for the negative t result.