Question 1037661
Simplify and use Rational Roots Theorem.


{{{6x^3-3x^2-2x+1=0}}}


List of roots to check are pos and neg  1/6, 1/2, 1/3, 1.  You use synthetic division for these checks.



{{{1/2}}} is one of the roots, meaning a binomial factor is  {{{(x-1/2)}}}.  This leaves a quadratic factor still to analyze, so you could apply general solution formula for quadratic equation.