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Solve `sin^2x +1/4sin^2 3x=sinxsin^2 3x`

Answer» `sin^2x+1/4sin^2 2x=sinxsin^2 3x`
`sin^2x-sinxsin^2 3x+1/4sin^2 3x=0`
`(sinx-1/2sin^2 3x)^2-1/4sin^4 3x+1/4sin^2 3x=0`
`(sinx-1/2sin^2 3x)^2+1/4sin^2 3x[-sin^2 3x+1]=0`
`(sinx-1/2sin^2 3x)^2+1/4sin^2 3xcos^2 3x=0`
`(sinx-1/2sin^2 3x)^2+1/4*(sin^2 6x)/4=0`
`(sinx-1/2sin^2 3x)^2+1/16sin^2 6x=0`
`(sinx-1/2sin^2 3x)^2+(1/4sin6x)^2=0`
`sinx-1/2sin^2 3x=0`
`2sinx=sin^2 3x`
`2sinx=sin^2((npi)/2)`
`x=0`
`(sin(6x)/4)=0`
`sin6x=0`
`6x=npi`
`x=(npi)/6`
`sinx=1/2`
`sinx=sinpi/6`
`x=npi+(-1)^n pi/6`.


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