`a)x(x+6)-7x-42=0`
`⇔x(x+6)-(7x+42)=0`
`⇔x(x+6)-7(x+6)=0`
`⇔(x+6)(x-7)=0`
`⇔`$\left[\begin{matrix} x+6=0\\ x-7=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=-6\\ x=7\end{matrix}\right.$
Vậy `x∈{-6;7}`
`b)x^4-2x³+10x²-20x=0`
`⇔x(x³-2x²+10x-20)=0`
`⇔x[(x^3-2x^2)+(10x-20)]=0`
`⇔x[x^2(x-2)+10(x-2)]=0`
`⇔x(x-2)(x^2+10)=0`
Ta có:`x²≥0∀x`
`⇒x²+10≥10>0∀x`
`⇒` vô nghiệm
`⇔x(x-2)=0`
`⇔`$\left[\begin{matrix} x=0\\ x-2=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=0\\ x=2\end{matrix}\right.$
Vậy `x∈{0;2}`
`c)x³+27+(x+3)(x-9)=0`
`⇔(x³+27)+(x+3)(x-9)=0`
`⇔(x+3)(x²-3x+9)+(x+3)(x-9)=0`
`⇔(x+3)(x²-3x+9+x-9)=0`
`⇔(x+3)(x²-2x)=0`
`⇔x(x+3)(x-2)=0`
`⇔`$\left[\begin{matrix} x=0\\ x+3=0\\x-2=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=0\\ x=-3\\x=2\end{matrix}\right.$
Vậy `x∈{0;-3;2}`
`d)(2x-3)²=(x+5)²`
`⇔(2x-3)²-(x+5)²=0`
`⇔[(2x-3)+(x+5)][(2x-3)-(x+5)]=0`
`⇔(2x-3+x+5)(2x-3-x-5)=0`
`⇔(3x+2)(x-8)=0`
`⇔`$\left[\begin{matrix} 3x+2=0\\ x-8=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=-\dfrac{2}{3}\\ x=8\end{matrix}\right.$
Vậy `x∈{-2/3;8}`
`e)x²(x-1)-4x²+8x-4=0`
`⇔x²(x-1)-4(x²-2x+1)=0`
`⇔x²(x-1)-4(x-1)²=0`
`⇔(x-1)[x²-4(x-1)]=0`
`⇔(x-1)(x²-4x+4)=0`
`⇔(x-1)(x-2)²=0`
`⇔`$\left[\begin{matrix} x-1=0\\ (x-2)²=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=1\\ x-2=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=1\\ x=2\end{matrix}\right.$
Vậy `x∈{1;2}`
