`(4x^2-25)^2-9(2x-5)^2=0`
`⇔[(2x-5)(2x+5)]^2-9(2x-5)^2=0`
`⇔(2x-5)^2(2x+5)^2-9(2x-5)^2=0`
`⇔(2x-5)^2[(2x+5)^2-9]=0`
`⇔(2x-5)^2(2x+5+3)(2x+5-3)=0`
`⇔(2x-5)^2(2x+8)(2x+2)=0`
\(⇔\left[ \begin{array}{l}(2x-5)^2=0\\2x+8=0\\2x+2=0\end{array} \right.⇔\left[ \begin{array}{l}x=\dfrac52\\x=-4\\x=-1\end{array} \right.\)