Question 131109
{{{4x+x(x-1)=0}}} Start with the given equation



{{{4x+x^2-x=0}}} Distribute




{{{x^2+3x=0}}} Combine like terms




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




Now set each factor equal to zero:

{{{x=0}}} or  {{{x+3=0}}} 


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




So our solutions are 


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



which means that the x-intercepts are


(-3,0) and (0,0)




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



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