`1)5(x+3)-2x(3+x)=0`
`⇔5(x+3)-2x(x+3)=0`
`⇔(x+3)(5-2x)=0`
`⇔`$\left[\begin{matrix} x+3=0\\ 5-2x=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=-3\\ x=\dfrac{5}{2}\end{matrix}\right.$
Vậy `x∈{-3;5/2}`
`2)4x(x-2004)-x+2004=0`
`⇔4x(x-2004)-(x-2004)=0`
`⇔(x-2004)(4x-1)=0`
`⇔`$\left[\begin{matrix} x-2004=0\\ 4x-1=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=2004\\ x=\dfrac{1}{4}\end{matrix}\right.$
Vậy `x∈{2004;1/4}`
`3)(x+1)²=x+1`
`⇔(x+1)²-(x+1)=0`
`⇔(x+1)(x+1-1)=0`
`⇔x(x+1)=0`
`⇔`$\left[\begin{matrix} x=0\\ x+1=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=0\\ x=-1\end{matrix}\right.$
Vậy `x∈{0;-1}`
`4)(x-4)²-36=0`
`⇔(x-4)²-6²=0`
`⇔(x-4+6)(x-4-6)=0`
`⇔(x+2)(x-10)=0`
`⇔`$\left[\begin{matrix} x+2=0\\ x-10=0\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=-2\\ x=10\end{matrix}\right.$
Vậy `x∈{-2;10}`
`5)(x+8)²=121`
`⇔(x+8)²=11²`
`⇔`$\left[\begin{matrix} x+8=11\\ x+8=-11\end{matrix}\right.$
`⇔`$\left[\begin{matrix} x=3\\ x=-19\end{matrix}\right.$
Vậy `x∈{3;-19}`
`6)x²+8x+16=0`
`⇔x²+2.x.4+4²=0`
`⇔(x+4)²=0`
`⇔x+4=0`
`⇔x=-4`
Vậy `x=-4`
`7)4x²-12x=-9`
`⇔4x²-12x+9=0`
`⇔(2x)²-2.2x.3+3²=0`
`⇔(2x-3)²=0`
`⇔2x-3=0`
`⇔2x=3`
`⇔x=3/2`
Vậy `x=3/2`
