\(4x^2-4x-24\)

\(=\left(4x^2-12x\right)+\left(8x-24\right)\)

\(=4x\left(x-3\right)+8\left(x-3\right)\)

\(=\left(4x+8\right)\left(x-3\right)\)

\(=4\left(x+2\right)\left(x-3\right)\)

\(x^2-14x=-24\)

\(\Leftrightarrow x^2-14+24=0\)

\(\Leftrightarrow x^2-12x-2x+24=0\)

\(\Leftrightarrow x\left(x-12\right)-2\left(x-12\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-12\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x-12=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=12\end{matrix}\right.\)