Parameter Matrix Determinant $A=\begin{bmatrix} 7x+42&x-21&x-21&x-21&x-21\\x-21&7x+42&x-21&x-21&x-21\\x-21&x-21&7x+42&x-21&x-21\\x-21&x-21&x-21&7x+42&x-21\\x-21&x-21&x-21&x-21&7x+42\end{bmatrix}$
I am trying to find the determinant of $A$, so far without success. I tried reducing it to a triangular matrix but wasn't successful. I would greatly appreciate any help.

HINT: Calculate the eigenvalues of $A=(x-21)O + (6x+63)I$, where $O$ is a matrix full of $1$s and $I$ is the unit matrix...
