Question 483457
Alternate forms:

{{{x^4-5x^3-25x^2+65x+84>=0}}}...replace {{{-5x^3}}} with {{{5x^3-10x^3}}},  {{{-25x^2}}} with {{{4x^2 +21x^2-50x^2}}}, and {{{65x}}} with {{{-40x+105x}}}

{{{x^4+5x^3-10x^3+4x^2 +21x^2-50x^2-40x+105x+84>=0}}}...rearrange the terms

{{{(x^4+5x^3+4x^2) -(10x^3+50x^2+40x) +(21x^2+105x+84)>=0}}}

{{{x^2(x^2+5x+4) -10x(x^2+5x+4) +21(x^2+5x+4)>=0}}}

{{{(x^2 -10x +21)(x^2+5x+4)>=0}}}...replace {{{-10x }}} with {{{-7x-3x}}}

{{{(x^2 -7x-3x +21)(x^2+5x+4)>=0}}}

{{{((x^2 -7x)-(3x -21))(x^2+5x+4)>=0}}}replace {{{5x }}} with {{{x+4x}}}


{{{(x(x -7)-3(x -7))(x^2+x+4x+4)>=0}}}

{{{(x-3)(x -7)((x^2+x)+(4x+4))>=0}}}

{{{(x-3)(x -7)(x(x+1)+4(x+1))>=0}}}

{{{(x-3)(x -7)(x+4)(x+1)>=0}}}


Solutions:
x>=7
-1<=x<=3
x<=-4

Integer solutions:
x = ±1
x = 0
x = 2
x = 3