\(x\left(4x^2-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\2x-1=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
\(a,4x^3-x=0\\ \Leftrightarrow x\left(4x^2-1\right)=0\\ \Leftrightarrow x\left(2x-1\right)\left(2x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
\(b,\left(x+1\right)\left(x^2-x+1\right)-x\left(x-2\right)\left(x+2\right)=21\\ \Leftrightarrow x^3+1-x\left(x^2-4\right)=21\\ \Leftrightarrow x^3+1-x^3+4x=21\\ \Leftrightarrow4x=20\\ \Leftrightarrow x=5\)
