Verified answer

[tex]\displaystyle\bf\\9x^{2} -(5x-3)^{2} =(1-4x)(1+4x)\\\\9x^{2} -(25x^{2} -30x+9)=1^{2} -(4x)^{2} \\\\9x^{2} -25x^{2} +30x-9=1-16x^{2} \\\\-16x^{2} +30x+16x^{2} =1+9\\\\30x=10\\\\x=\frac{1}{3}[/tex]