Đáp án:

$1) \left[\begin{array}{l} x=-\dfrac{1}{3}\\ x=-1\end{array} \right.\\ 2) \left[\begin{array}{l} x=-5\\ x=-1\end{array} \right.\\ 3) \left[\begin{array}{l} x=-3\\ x=\dfrac{1}{2}\end{array} \right.\\ 4) \left[\begin{array}{l} x=\dfrac{2}{5}\\x=\dfrac{-7 \pm \sqrt{217}}{12}\end{array} \right.\\ 5) \left[\begin{array}{l} x=4\\ x=1\\x=5\end{array} \right.\\ 6)\left[\begin{array}{l} x=-2\\ x=-\dfrac{1}{2}\\x=-1\end{array} \right.$

Giải thích các bước giải:

$1)4x^2+4x+1=x^2\\ \Leftrightarrow 3x^2+4x+1=0\\ \Leftrightarrow 3x^2+3x+x+1=0\\ \Leftrightarrow 3x(x+1)+x+1=0\\ \Leftrightarrow (3x+1)(x+1)=0\\ \Leftrightarrow \left[\begin{array}{l} 3x+1=0\\ x+1=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=-\dfrac{1}{3}\\ x=-1\end{array} \right.\\ 2)(x+5)(2+3x)=(x+5)x\\ \Leftrightarrow  (x+5)(2+3x)-(x+5)x=0\\ \Leftrightarrow  (x+5)(2+3x-x)=0\\ \Leftrightarrow  (x+5)(2+2x)=0\\ \Leftrightarrow  2(x+5)(x+1)=0\\ \Leftrightarrow \left[\begin{array}{l} x+5=0\\ x+1=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=-5\\ x=-1\end{array} \right.\\ 3)(x+3)(4-x)=x^2+6x+9\\ \Leftrightarrow (x+3)(4-x)=(x+3)^2\\ \Leftrightarrow (x+3)(4-x)-(x+3)^2=0\\ \Leftrightarrow (x+3)(4-x-x-3)=0\\ \Leftrightarrow (x+3)(1-2x)=0\\ \Leftrightarrow \left[\begin{array}{l} x+3=0\\ 1-2x=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=-3\\ x=\dfrac{1}{2}\end{array} \right.\\ 4)(2-5x)(6x^2+7x-8)=5x-2\\ \Leftrightarrow (2-5x)(6x^2+7x-8)-(5x-2)=0\\ \Leftrightarrow (2-5x)(6x^2+7x-8)+(2-5x)=0\\ \Leftrightarrow (2-5x)(6x^2+7x-8+1)=0\\ \Leftrightarrow (2-5x)(6x^2+7x-7)=0\\ \Leftrightarrow (2-5x)\left((\sqrt{6}x)^2+2.\sqrt{6}x.\dfrac{7\sqrt{6}}{12}+\dfrac{49}{24}-\dfrac{217}{24}\right)=0\\ \Leftrightarrow (2-5x)\left(\left(\sqrt{6}x+\dfrac{7\sqrt{6}}{12}\right)^2-\sqrt{\dfrac{217}{24}}^2\right)=0\\ \Leftrightarrow (2-5x)\left(\sqrt{6}x+\dfrac{7\sqrt{6}}{12}-\sqrt{\dfrac{217}{24}}\right)\left(\sqrt{6}x+\dfrac{7\sqrt{6}}{12}-\sqrt{\dfrac{217}{24}}\right)=0\\ \Leftrightarrow \left[\begin{array}{l} x=\dfrac{2}{5}\\x=\dfrac{-7 \pm \sqrt{217}}{12}\end{array} \right.\\ 5)(4-x)(x^2-7x+1)=x^2-16\\ \Leftrightarrow (4-x)(x^2-7x+1)=(x-4)(x+4)\\ \Leftrightarrow (4-x)(x^2-7x+1)-(x-4)(x+4)=0\\ \Leftrightarrow (4-x)(x^2-7x+1)+(4-x)(x+4)=0\\ \Leftrightarrow (4-x)(x^2-7x+1+x+4)=0\\ \Leftrightarrow (4-x)(x^2-6x+5)=0\\ \Leftrightarrow (4-x)(x^2-5x-x+5)=0\\ \Leftrightarrow (4-x)\left(x(x-5)-(x-5)\right)=0\\ \Leftrightarrow (4-x)(x-1)(x-5)=0\\ \Leftrightarrow \left[\begin{array}{l} 4-x=0\\ x-1=0\\x-5=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=4\\ x=1\\x=5\end{array} \right.\\ 6)2x^3+7x^2+7x+2=0\\ \Leftrightarrow 2x^3+4x^2+3x^2+6x+x+2=0\\ \Leftrightarrow 2x^2(x+2)+3x(x+2)+x+2=0\\ \Leftrightarrow (x+2)(2x^2+3x+1)=0\\ \Leftrightarrow (x+2)(2x^2+2x+x+1)=0\\ \Leftrightarrow (x+2)(2x(x+1)+x+1)=0\\ \Leftrightarrow (x+2)(2x+1)(x+1)=0\\ \Leftrightarrow \left[\begin{array}{l} x+2=0\\ 2x+1=0\\x+1=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=-2\\ x=-\dfrac{1}{2}\\x=-1\end{array} \right.$