((6x+1)^3(27x^2+2)-(9x^3+2x)(3)(6x+1)^2(6))/(6x+1)^6

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Solution for ((6x+1)^3(27x^2+2)-(9x^3+2x)(3)(6x+1)^2(6))/(6x+1)^6 equation: 


D( x )

(6*x+1)^6 = 0

(6*x+1)^6 = 0

(6*x+1)^6 = 0

6*x+1 = 0 // - 1

6*x = -1 // : 6

x = -1/6

x in (-oo:-1/6) U (-1/6:+oo)

((6*x+1)^3*(27*x^2+2)-(3*6*(9*x^3+2*x)*(6*x+1)^2))/((6*x+1)^6) = 0

((6*x+1)^3*(27*x^2+2)-18*(9*x^3+2*x)*(6*x+1)^2)/((6*x+1)^6) = 0

(6*x+1)^3*(27*x^2+2)-18*(9*x^3+2*x)*(6*x+1)^2 = 0

(6*x+1)^3*(27*x^2+2)-18*(9*x^3+2*x)*(6*x+1)^2 = 0

972*x^4-540*x^3-189*x^2+2 = 0

972*x^4-540*x^3-189*x^2+2 = 0

972*x^4-540*x^3-189*x^2+2 = 0

{ 1, -1, 2, -2 }

1

x = 1

972*x^4-540*x^3-189*x^2+2 = 245

1

-1

x = -1

972*x^4-540*x^3-189*x^2+2 = 1325

-1

2

x = 2

972*x^4-540*x^3-189*x^2+2 = 10478

2

-2

x = -2

972*x^4-540*x^3-189*x^2+2 = 19118

-2

{ 1/2, -1/2, 1/3, -1/3, 1/4, -1/4, 1/6, -1/6, 1/9, -1/9, 1/12, -1/12, 1/18, -1/18, 1/27, -1/27, 1/36, -1/36, 1/54, -1/54, 1/81, -1/81, 1/108, -1/108, 1/162, -1/162, 1/243, -1/243, 1/324, -1/324, 1/486, -1/486, 1/972, -1/972, -1/2, 1/2, -1/3, 1/3, -1/4, 1/4, -1/6, 1/6, -1/9, 1/9, -1/12, 1/12, -1/18, 1/18, -1/27, 1/27, -1/36, 1/36, -1/54, 1/54, -1/81, 1/81, -1/108, 1/108, -1/162, 1/162, -1/243, 1/243, -1/324, 1/324, -1/486, 1/486, -1/972, 1/972, 2/2, -2/2, 2/3, -2/3, 2/4, -2/4, 2/6, -2/6, 2/9, -2/9, 2/12, -2/12, 2/18, -2/18, 2/27, -2/27, 2/36, -2/36, 2/54, -2/54, 2/81, -2/81, 2/108, -2/108, 2/162, -2/162, 2/243, -2/243, 2/324, -2/324, 2/486, -2/486, 2/972, -2/972, -2/2, 2/2, -2/3, 2/3, -2/4, 2/4, -2/6, 2/6, -2/9, 2/9, -2/12, 2/12, -2/18, 2/18, -2/27, 2/27, -2/36, 2/36, -2/54, 2/54, -2/81, 2/81, -2/108, 2/108, -2/162, 2/162, -2/243, 2/243, -2/324, 2/324, -2/486, 2/486, -2/972, 2/972 }

1/2

x

1/2

972*x^4-540*x^3-189*x^2+2 = -52

1/2

-1/2

x

-1/2

972*x^4-540*x^3-189*x^2+2 = 83

-1/2

1/3

x

1/3

972*x^4-540*x^3-189*x^2+2 = -27

1/3

-1/3

x

-1/3

972*x^4-540*x^3-189*x^2+2 = 13

-1/3

1/4

x

1/4

972*x^4-540*x^3-189*x^2+2 = -14.453125

1/4

-1/4

x

-1/4

972*x^4-540*x^3-189*x^2+2 = 2.421875

-1/4

1/6

x

1/6

972*x^4-540*x^3-189*x^2+2 = -5

1/6

-1/6

x

-1/6

972*x^4-540*x^3-189*x^2+2 = 0

-1/6

x+1/6

972*x^3-702*x^2-72*x+12

972*x^4-540*x^3-189*x^2+2

x+1/6

-972*x^4-162*x^3

2-702*x^3-189*x^2

702*x^3+117*x^2

2-72*x^2

72*x^2+12*x

12*x+2

-12*x-2

0

972*x^3-702*x^2-72*x+12 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }

1

x = 1

972*x^3-702*x^2-72*x+12 = 210

1

-1

x = -1

972*x^3-702*x^2-72*x+12 = -1590

-1

2

x = 2

972*x^3-702*x^2-72*x+12 = 4836

2

-2

x = -2

972*x^3-702*x^2-72*x+12 = -10428

-2

3

x = 3

972*x^3-702*x^2-72*x+12 = 19722

3

-3

x = -3

972*x^3-702*x^2-72*x+12 = -32334

-3

4

x = 4

972*x^3-702*x^2-72*x+12 = 50700

4

-4

x = -4

972*x^3-702*x^2-72*x+12 = -73140

-4

6

x = 6

972*x^3-702*x^2-72*x+12 = 184260

6

-6

x = -6

972*x^3-702*x^2-72*x+12 = -234780

-6

12

x = 12

972*x^3-702*x^2-72*x+12 = 1577676

12

-12

x = -12

972*x^3-702*x^2-72*x+12 = -1779828

-12

{ 1/2, -1/2, 1/3, -1/3, 1/4, -1/4, 1/6, -1/6, 1/9, -1/9, 1/12, -1/12, 1/18, -1/18, 1/27, -1/27, 1/36, -1/36, 1/54, -1/54, 1/81, -1/81, 1/108, -1/108, 1/162, -1/162, 1/243, -1/243, 1/324, -1/324, 1/486, -1/486, 1/972, -1/972, -1/2, 1/2, -1/3, 1/3, -1/4, 1/4, -1/6, 1/6, -1/9, 1/9, -1/12, 1/12, -1/18, 1/18, -1/27, 1/27, -1/36, 1/36, -1/54, 1/54, -1/81, 1/81, -1/108, 1/108, -1/162, 1/162, -1/243, 1/243, -1/324, 1/324, -1/486, 1/486, -1/972, 1/972, 2/2, -2/2, 2/3, -2/3, 2/4, -2/4, 2/6, -2/6, 2/9, -2/9, 2/12, -2/12, 2/18, -2/18, 2/27, -2/27, 2/36, -2/36, 2/54, -2/54, 2/81, -2/81, 2/108, -2/108, 2/162, -2/162, 2/243, -2/243, 2/324, -2/324, 2/486, -2/486, 2/972, -2/972, -2/2, 2/2, -2/3, 2/3, -2/4, 2/4, -2/6, 2/6, -2/9, 2/9, -2/12, 2/12, -2/18, 2/18, -2/27, 2/27, -2/36, 2/36, -2/54, 2/54, -2/81, 2/81, -2/108, 2/108, -2/162, 2/162, -2/243, 2/243, -2/324, 2/324, -2/486, 2/486, -2/972, 2/972, 3/2, -3/2, 3/3, -3/3, 3/4, -3/4, 3/6, -3/6, 3/9, -3/9, 3/12, -3/12, 3/18, -3/18, 3/27, -3/27, 3/36, -3/36, 3/54, -3/54, 3/81, -3/81, 3/108, -3/108, 3/162, -3/162, 3/243, -3/243, 3/324, -3/324, 3/486, -3/486, 3/972, -3/972, -3/2, 3/2, -3/3, 3/3, -3/4, 3/4, -3/6, 3/6, -3/9, 3/9, -3/12, 3/12, -3/18, 3/18, -3/27, 3/27, -3/36, 3/36, -3/54, 3/54, -3/81, 3/81, -3/108, 3/108, -3/162, 3/162, -3/243, 3/243, -3/324, 3/324, -3/486, 3/486, -3/972, 3/972, 4/2, -4/2, 4/3, -4/3, 4/4, -4/4, 4/6, -4/6, 4/9, -4/9, 4/12, -4/12, 4/18, -4/18, 4/27, -4/27, 4/36, -4/36, 4/54, -4/54, 4/81, -4/81, 4/108, -4/108, 4/162, -4/162, 4/243, -4/243, 4/324, -4/324, 4/486, -4/486, 4/972, -4/972, -4/2, 4/2, -4/3, 4/3, -4/4, 4/4, -4/6, 4/6, -4/9, 4/9, -4/12, 4/12, -4/18, 4/18, -4/27, 4/27, -4/36, 4/36, -4/54, 4/54, -4/81, 4/81, -4/108, 4/108, -4/162, 4/162, -4/243, 4/243, -4/324, 4/324, -4/486, 4/486, -4/972, 4/972, 6/2, -6/2, 6/3, -6/3, 6/4, -6/4, 6/6, -6/6, 6/9, -6/9, 6/12, -6/12, 6/18, -6/18, 6/27, -6/27, 6/36, -6/36, 6/54, -6/54, 6/81, -6/81, 6/108, -6/108, 6/162, -6/162, 6/243, -6/243, 6/324, -6/324, 6/486, -6/486, 6/972, -6/972, -6/2, 6/2, -6/3, 6/3, -6/4, 6/4, -6/6, 6/6, -6/9, 6/9, -6/12, 6/12, -6/18, 6/18, -6/27, 6/27, -6/36, 6/36, -6/54, 6/54, -6/81, 6/81, -6/108, 6/108, -6/162, 6/162, -6/243, 6/243, -6/324, 6/324, -6/486, 6/486, -6/972, 6/972, 12/2, -12/2, 12/3, -12/3, 12/4, -12/4, 12/6, -12/6, 12/9, -12/9, 12/12, -12/12, 12/18, -12/18, 12/27, -12/27, 12/36, -12/36, 12/54, -12/54, 12/81, -12/81, 12/108, -12/108, 12/162, -12/162, 12/243, -12/243, 12/324, -12/324, 12/486, -12/486, 12/972, -12/972, -12/2, 12/2, -12/3, 12/3, -12/4, 12/4, -12/6, 12/6, -12/9, 12/9, -12/12, 12/12, -12/18, 12/18, -12/27, 12/27, -12/36, 12/36, -12/54, 12/54, -12/81, 12/81, -12/108, 12/108, -12/162, 12/162, -12/243, 12/243, -12/324, 12/324, -12/486, 12/486, -12/972, 12/972 }

1/2

x

1/2

972*x^3-702*x^2-72*x+12 = -78

1/2

-1/2

x

-1/2

972*x^3-702*x^2-72*x+12 = -249

-1/2

1/3

x

1/3

972*x^3-702*x^2-72*x+12 = -54

1/3

-1/3

x

-1/3

972*x^3-702*x^2-72*x+12 = -78

-1/3

1/4

x

1/4

972*x^3-702*x^2-72*x+12 = -34.6875

1/4

-1/4

x

-1/4

972*x^3-702*x^2-72*x+12 = -29.0625

-1/4

1/6

x

1/6

972*x^3-702*x^2-72*x+12 = -15

1/6

-1/6

x

-1/6

972*x^3-702*x^2-72*x+12 = 0

-1/6

x+1/6

972*x^2-864*x+72

972*x^3-702*x^2-72*x+12

x+1/6

-972*x^3-162*x^2

12-864*x^2-72*x

864*x^2+144*x

72*x+12

-72*x-12

0

972*x^2-864*x+72 = 0

DELTA = (-864)^2-(4*72*972)

DELTA = 466560

DELTA > 0

x = (466560^(1/2)+864)/(2*972) or x = (864-466560^(1/2))/(2*972)

x = (216*10^(1/2)+864)/1944 or x = (864-216*10^(1/2))/1944

x in { (864-216*10^(1/2))/1944, (216*10^(1/2)+864)/1944, -1/6, -1/6} 

(x-((864-216*10^(1/2))/1944))*(x-((216*10^(1/2)+864)/1944))*(x+1/6)^2 = 0

(x-((864-216*10^(1/2))/1944))*(x-((216*10^(1/2)+864)/1944))*(x+1/6)^2 = 0

((x-((864-216*10^(1/2))/1944))*(x-((216*10^(1/2)+864)/1944))*(x+1/6)^2)/((6*x+1)^6) = 0

( x+1/6 )

x+1/6 = 0 // - 1/6

x = -1/6

( x-((216*10^(1/2)+864)/1944) )

x-((216*10^(1/2)+864)/1944) = 0 // + (216*10^(1/2)+864)/1944

x = (216*10^(1/2)+864)/1944

( x-((864-216*10^(1/2))/1944) )

x-((864-216*10^(1/2))/1944) = 0 // + (864-216*10^(1/2))/1944

x = (864-216*10^(1/2))/1944

x in { -1/6} 

x in { (216*10^(1/2)+864)/1944, (864-216*10^(1/2))/1944 }

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