`5.`\(\left(x+3\right)^2-\left(x-2\right)\left(x+5\right)=9\)
\(\Rightarrow x^2+6x+9-x^2-5x+2x+10-9=0\)
\(\Rightarrow3x+10=0\)
\(\Rightarrow x=-\dfrac{10}{3}\)
`6.`\(3x-\left(x+1\right)\left(x^2-x+1\right)+x\left(x^2-4\right)=5\)
\(\Rightarrow3x-x^3-1+x^3-4x-5=0\)
\(\Rightarrow-x-6=0\)
\(\Rightarrow x=-6\)
`7.`\(x^2-2x=24\)
\(\Rightarrow x^2-2x-24=0\)
\(\Rightarrow\left(x-6\right)\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\)
`8.`\(x^3+6x^2+12x=19\)
\(\Rightarrow\left(x^3-x^2\right)+\left(7x^2-7x\right)+\left(19x-19\right)=0\)
\(\Rightarrow x^2\left(x-1\right)+7x\left(x-1\right)+19\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x^2+7x+19\right)=0\)
\(\Rightarrow x-1=0\)
`=>x=1`
5.
\(\Leftrightarrow x^2+6x+9-\left(x^2+3x-10\right)=9\)
\(\Leftrightarrow3x+19=9\)
\(\Leftrightarrow3x=-10\)
\(\Leftrightarrow x=-\dfrac{10}{3}\)
6.
\(\Leftrightarrow3x-\left(x^3+1\right)+x^3-4x=5\)
\(\Leftrightarrow-x-1=5\)
\(\Leftrightarrow x=-6\)
7.
\(\Leftrightarrow x^2-2x-24=0\)
\(\Leftrightarrow x^2-6x+4x-24=0\)
\(\Leftrightarrow x\left(x-6\right)+4\left(x-6\right)=0\)
\(\Leftrightarrow\left(x-6\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\x+4=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\)
8.
\(x^3+6x^2+12x=19\)
\(\Leftrightarrow x^3+6x^2+12x+8=27\)
\(\Leftrightarrow\left(x+2\right)^3=3^3\)
\(\Leftrightarrow x+2=3\)
\(\Leftrightarrow x=1\)
