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D( x )
x^2-(6*x)+36 = 0
x+6 = 0
x^3+216 = 0
x^2-(6*x)+36 = 0
x^2-(6*x)+36 = 0
x^2-6*x+36 = 0
x^2-6*x+36 = 0
DELTA = (-6)^2-(1*4*36)
DELTA = -108
DELTA < 0
x+6 = 0
x+6 = 0
x+6 = 0 // - 6
x = -6
x^3+216 = 0
x^3+216 = 0
1*x^3 = -216 // : 1
x^3 = -216
x^3 = -216 // ^ 1/3
x = -6
x in (-oo:-6) U (-6:+oo)
6/(x+6)+7/(x^2-(6*x)+36) = 648/(x^3+216) // - 648/(x^3+216)
6/(x+6)+7/(x^2-(6*x)+36)-(648/(x^3+216)) = 0
6/(x+6)+7/(x^2-6*x+36)-648*(x^3+216)^-1 = 0
6/(x+6)+7/(x^2-6*x+36)-648/(x^3+216) = 0
x^2-6*x+36 = 0
x^2-6*x+36 = 0
x^2-6*x+36 = 0
DELTA = (-6)^2-(1*4*36)
DELTA = -108
DELTA < 0
1 = 0
6/(x+6)-648/(x^3+216)+7 = 0
(6*(x^3+216))/((x+6)*(x^3+216))+(7*(x+6)*(x^3+216))/((x+6)*(x^3+216))+(-648*(x+6))/((x+6)*(x^3+216)) = 0
6*(x^3+216)+7*(x+6)*(x^3+216)-648*(x+6) = 0
7*x^4+48*x^3+1512*x-648*x-3888+10368 = 0
7*x^4+48*x^3+864*x+6480 = 0
7*x^4+48*x^3+864*x+6480 = 0
7*x^4+48*x^3+864*x+6480 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 8, -8, 9, -9, 10, -10, 12, -12, 15, -15, 16, -16, 18, -18, 20, -20, 24, -24, 27, -27, 30, -30, 36, -36, 40, -40, 45, -45, 48, -48, 54, -54, 60, -60, 72, -72, 80, -80, 81, -81, 90, -90, 108, -108, 120, -120, 135, -135, 144, -144, 162, -162, 180, -180, 216, -216, 240, -240, 270, -270, 324, -324, 360, -360, 405, -405, 432, -432, 540, -540, 648, -648, 720, -720, 810, -810, 1080, -1080, 1296, -1296, 1620, -1620, 2160, -2160, 3240, -3240, 6480, -6480 }
1
x = 1
7*x^4+48*x^3+864*x+6480 = 7399
1
-1
x = -1
7*x^4+48*x^3+864*x+6480 = 5575
-1
2
x = 2
7*x^4+48*x^3+864*x+6480 = 8704
2
-2
x = -2
7*x^4+48*x^3+864*x+6480 = 4480
-2
3
x = 3
7*x^4+48*x^3+864*x+6480 = 10935
3
-3
x = -3
7*x^4+48*x^3+864*x+6480 = 3159
-3
4
x = 4
7*x^4+48*x^3+864*x+6480 = 14800
4
-4
x = -4
7*x^4+48*x^3+864*x+6480 = 1744
-4
5
x = 5
7*x^4+48*x^3+864*x+6480 = 21175
5
-5
x = -5
7*x^4+48*x^3+864*x+6480 = 535
-5
6
x = 6
7*x^4+48*x^3+864*x+6480 = 31104
6
-6
x = -6
7*x^4+48*x^3+864*x+6480 = 0
-6
x+6
7*x^3+6*x^2-36*x+1080
7*x^4+48*x^3+864*x+6480
x+6
-7*x^4-42*x^3
6*x^3+864*x+6480
-6*x^3-36*x^2
864*x-36*x^2+6480
36*x^2+216*x
1080*x+6480
-1080*x-6480
0
7*x^3+6*x^2-36*x+1080 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 8, -8, 9, -9, 10, -10, 12, -12, 15, -15, 18, -18, 20, -20, 24, -24, 27, -27, 30, -30, 36, -36, 40, -40, 45, -45, 54, -54, 60, -60, 72, -72, 90, -90, 108, -108, 120, -120, 135, -135, 180, -180, 216, -216, 270, -270, 360, -360, 540, -540, 1080, -1080 }
1
x = 1
7*x^3+6*x^2-36*x+1080 = 1057
1
-1
x = -1
7*x^3+6*x^2-36*x+1080 = 1115
-1
2
x = 2
7*x^3+6*x^2-36*x+1080 = 1088
2
-2
x = -2
7*x^3+6*x^2-36*x+1080 = 1120
-2
3
x = 3
7*x^3+6*x^2-36*x+1080 = 1215
3
-3
x = -3
7*x^3+6*x^2-36*x+1080 = 1053
-3
4
x = 4
7*x^3+6*x^2-36*x+1080 = 1480
4
-4
x = -4
7*x^3+6*x^2-36*x+1080 = 872
-4
5
x = 5
7*x^3+6*x^2-36*x+1080 = 1925
5
-5
x = -5
7*x^3+6*x^2-36*x+1080 = 535
-5
6
x = 6
7*x^3+6*x^2-36*x+1080 = 2592
6
-6
x = -6
7*x^3+6*x^2-36*x+1080 = 0
-6
x+6
7*x^2-36*x+180
7*x^3+6*x^2-36*x+1080
x+6
-7*x^3-42*x^2
1080-36*x^2-36*x
36*x^2+216*x
180*x+1080
-180*x-1080
0
7*x^2-36*x+180 = 0
DELTA = (-36)^2-(4*7*180)
DELTA = -3744
DELTA < 0
x in { -6, -6}
(x+6)^2 = 0
((x+6)^2)/((x+6)*(x^3+216)) = 0
((x+6)^2)/((x+6)*(x^3+216)) = 0 // * (x+6)*(x^3+216)
(x+6)^2 = 0
x+6 = 0 // - 6
x = -6
x in { -6}
x belongs to the empty set
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