Đáp án:

$a) \left[\begin{array}{l} x=1\\x=-\dfrac{1}{3}\end{array} \right.\\ b) x=-1\\ c) x=\dfrac{-11}{25}\\ d)\left[\begin{array}{l} x=7\\x=-3\end{array} \right.\\ e) \left[\begin{array}{l} x=\dfrac{9}{2}\\x=\dfrac{1}{2}\end{array} \right.\\ f) x=\dfrac{2}{15}$

Giải thích các bước giải:

$a)9x^2-6x-3=0\\ \Leftrightarrow 9x^2-6x+1-4=0\\ \Leftrightarrow (3x-1)^2-2^2=0\\ \Leftrightarrow (3x-1-2)(3x-1+2)=0\\ \Leftrightarrow (3x-3)(3x+1)=0\\ \Leftrightarrow \left[\begin{array}{l} 3x-3=0\\3x+1=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=1\\x=-\dfrac{1}{3}\end{array} \right.\\ b)x^3+9x^2+27x+19=0\\ \Leftrightarrow x^3+3.x^2.3+3.x.3^2+3^3-8=0\\ \Leftrightarrow (x+3)^3-2^3=0\\ \Leftrightarrow (x+3-2)\left((x+3)^2+2(x+3)+2^2\right)=0\\ \Leftrightarrow (x+1)\left((x+3)^2+2(x+3)+1+3\right)=0\\ \Leftrightarrow (x+1)\left((x+3+1)^2+3\right)=0\\ \Leftrightarrow (x+1)\left((x+4)^2+3\right)=0\\ \Leftrightarrow x+1=0\\ \Leftrightarrow x=-1\\ c)x(x-5)(x+5)-(x+2)(x^2-2x+4)=3\\ \Leftrightarrow x(x^2-25)-(x^3+2^3)=3\\ \Leftrightarrow x^3-25x-x^3-8=3\\ \Leftrightarrow -25x=11\\ \Leftrightarrow x=\dfrac{-11}{25}\\ d)x^2-4x+4=25\\ \Leftrightarrow (x-2)^2-25=0\\ \Leftrightarrow (x-2)^2-5^2=0\\ \Leftrightarrow (x-2-5)(x-2+5)=0\\ \Leftrightarrow (x-7)(x+3)=0\\ \Leftrightarrow \left[\begin{array}{l} x-7=0\\x+3=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=7\\x=-3\end{array} \right.\\ e)(5-2x)^2-16=0\\ \Leftrightarrow (2x-5)^2-16=0\\ \Leftrightarrow (2x-5)^2-4^2=0\\ \Leftrightarrow (2x-5-4)(2x-5+4)=0\\ \Leftrightarrow (2x-9)(2x-1)=0\\ \Leftrightarrow \left[\begin{array}{l} 2x-9=0\\2x-1=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=\dfrac{9}{2}\\x=\dfrac{1}{2}\end{array} \right.\\ f)(x-3)^3-(x-3)(x^2+3x+9)+9(x+1)^2=15\\ \Leftrightarrow x^3-9x^2+27x-27-(x^3-3^3)+9(x^2+2x+1)=15\\ \Leftrightarrow x^3-9x^2+27x-27-x^3+27+9x^2+18x+9-15=0\\ \Leftrightarrow 45x-6=0\\ \Leftrightarrow x=\dfrac{2}{15}$