Question 180700

{{{9x^4-24x^3+16x^2=0}}} Start with the given equation



{{{x^2(9x^2-24x+16)=0}}} Factor out the GCF {{{x^2}}}



{{{x^2(3x-4)(3x-4)=0}}} Factor the inner expression by use of the difference of squares formula.



Now set each factor equal to zero:


{{{x^2=0}}}, {{{3x-4=0}}} or {{{3x-4=0}}}



{{{x=0}}}, {{{x=0}}}, {{{x=4/3}}} or {{{x=4/3}}}   Now solve for x in each case



Since we have repeating answers, our real answers are {{{x=0}}} or  {{{x=4/3}}} 



So the solutions are {{{x=0}}} or  {{{x=4/3}}}