[tex]f(x)=x^4+5x^2-5x^3-6+5x\\\\
Sorting\ equation:\\
f(x)=x^4-5x^3+5x^2+5x-6\\\\
Write\ 5x^2\ as\ -x^2+6x^2\ \ to\ factor\ equation:\\\\
f(x)=x^4-5x^3+-x^2+6x^2+5x-6\\
f(x)=x^2(x^2-1)-5x(x^2-1)+6(x^2-1)\\
f(x)=(x^2-5x+6)(x^2-1)\\
From\ first\ bracket\ write\ -5x\ as\ -2x-3x\\
f(x)=(x^2-2x-3x+6)(x^2-1)\\
f(x)=(x(x-2)-3(x-2))(x-1)(x+1)\\
f(x)=(x-2)(x-3)(x-1)(x+1)\\\\
To\ find\ roots\ compare\ equation\ to\ 0:\\
(x-2)(x-3)(x-1)(x+1)=0\\
x-2=0\ \ or\ \ x-3=0\ \ or\ \ x-1=0\ \ or\ \ x+1=0 [/tex][tex]x=2\ \ or\ \ x=3\ \ or\ \ x=1\ \ or\ \ x=-1.\\\\
Solution:\\
x\in\{-1,1,2,3\}[/tex]
