Question 152626
{{{9y^4 - 4y^2 = 0}}} Start with the given equation.



{{{y^2(9y^2 - 4) = 0}}} Factor out {{{y^2}}}



{{{y^2(3y+2)(3y-2) = 0}}} Factor {{{9y^2 - 4}}} to get {{{(3y+2)(3y-2)}}}




Now set each factor equal to zero:



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



Now solve for y for each equation:



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



So the solutions are {{{y=0}}} (with a multiplicity of 2), {{{y=-2/3}}} or {{{y=2/3}}}