Question 180698


{{{8x^4-18x^2=0}}} Start with the given equation



{{{2x^2(4x^2-9)=0}}} Factor out the GCF {{{2x^2}}}



{{{2x^2(2x+3)(2x-3)=0}}} Factor {{{4x^2-9}}} to get {{{(2x+3)(2x-3)}}} (use the difference of squares)



Now set each factor equal to zero:


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



{{{x=0}}}, {{{x=-3/2}}} or {{{x=3/2}}}   Now solve for x in each case



So the solutions are: 


 {{{x=0}}}, {{{x=-3/2}}} or {{{x=3/2}}}