Question 144984

{{{3x^2-x=0}}} Start with the given equation


{{{x(3x-1)=0}}} Factor the left side 



Now set each factor equal to zero:

{{{x=0}}} or  {{{3x-1=0}}} 


{{{x=0}}} or  {{{x=1/3}}}    Now solve for x in each case



So our answers are 


 {{{x=0}}} or  {{{x=1/3}}} 



Notice if we graph {{{y=3x^2-x}}}  we can see that the roots are {{{x=0}}} and  {{{x=1/3}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, 3x^2-x) }}}