\(\left(2x-1\right)\left(2x-3\right)\left(x+1\right)^2=18\)
\(\Leftrightarrow\left(2x-1\right)\left(2x-3\right)\left(2x+2\right)^2=72\) (*)
Đặt \(a=2x+2\)
(*) \(\Leftrightarrow\left(a-3\right)\left(a-5\right).a^2=0\)
\(\Leftrightarrow\left(a^3-5a^2\right)\left(a-3\right)=0\)
\(\Leftrightarrow a^4-8a^3+15a^2=0\)
\(\Leftrightarrow a^4-5a^3-3a^3+15a^2=0\)
\(\Leftrightarrow a^3.\left(a-5\right)-3a^2.\left(a-5\right)=0\)
\(\Leftrightarrow\left(a-5\right)\left(a-3\right).a^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\2x-1=0\\\left(2x+2\right)^2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{2}\\x=-1\end{matrix}\right.\)
