$\begin{array}{l}
A = \left\{ {x \in \mathbb{N}|\left( {{x^2} - 10x + 21} \right){x^3} = 0} \right\}\\
+ \left( {{x^2} - 10x + 21} \right){x^3} = 0\\
\Leftrightarrow \left( {x - 7} \right)\left( {x - 3} \right){x^3} = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 7\\
x = 3\\
x = 0
\end{array} \right.\\
\Rightarrow A = \left\{ {7;3;0} \right\}
\end{array}$