Answer: \(x=-1,2,3,6\).

The equation

\(\left|x^2-5x\right|=6\)

means that the expression inside the modulus is either \(6\) or \(-6\).

First solve

\(x^2-5x=6.\)

This gives

\(x^2-5x-6=0,\)

so

\((x-6)(x+1)=0.\)

Hence

\(x=6\quad\text{or}\quad x=-1.\)

Now solve

\(x^2-5x=-6.\)

This gives

\(x^2-5x+6=0,\)

so

\((x-2)(x-3)=0.\)

Hence

\(x=2\quad\text{or}\quad x=3.\)

Therefore the complete set of solutions is

\(x=-1,\ 2,\ 3,\ 6.\)