\(\Leftrightarrow\left[x\left(x+1\right)\right]\left[\left(x-1\right)\left(x+2\right)\right]=24\)
\(\Leftrightarrow\left(x^2+x\right)\left(x^2+x-2\right)-24=0\)
Đặt t=\(x^2+x-1\)
\(\Rightarrow x^2+x=t+1\)
\(\Rightarrow x^2+x-2=t-1\)
\(\Leftrightarrow\left(t+1\right)\left(t-1\right)-24=0\)
\(\Leftrightarrow t^2-1-24=0\)
\(\Leftrightarrow\left(t-5\right)\left(t+5\right)=0\)
\(\Rightarrow\left(x^2+x-1-5\right)\left(x^2+x-1+5\right)=0\)\(\Leftrightarrow\left(x^2+x-6\right)\left(x^2+x+4\right)=0\)
Vì \(x^2+x+4=x^2+2.\frac{1}{2}x+\frac{1}{4}+4-\frac{1}{4}\)
\(=\left(x+\frac{1}{2}\right)^2+\frac{15}{4}>0\)
nên \(x^2+x+4\ne0\)
Vậy nên \(x^2+x-6=0\)
\(\Leftrightarrow x^2-2x+3x-6=0\)
\(\Leftrightarrow x\left(x-2\right)+3\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+3\right)=0\)
\(\Rightarrow x=2\) hoặc \(x=-3\)
Vậy tập nghiệm của phương trình là S=\(\left\{2;-3\right\}\)