((12x^5)+(4x^4)-(24x^2)-8x)/(3x+1)

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Solution for ((12x^5)+(4x^4)-(24x^2)-8x)/(3x+1) equation: 


D( x )

3*x+1 = 0

3*x+1 = 0

3*x+1 = 0

3*x+1 = 0 // - 1

3*x = -1 // : 3

x = -1/3

x in (-oo:-1/3) U (-1/3:+oo)

(12*x^5+4*x^4-(24*x^2)-(8*x))/(3*x+1) = 0

(12*x^5+4*x^4-24*x^2-8*x)/(3*x+1) = 0

12*x^5+4*x^4-24*x^2-8*x = 0

4*x*(3*x^4+x^3-6*x-2) = 0

3*x^4+x^3-6*x-2

x^3*(3*x+1)-6*x-2

x^3*(3*x+1)-2*(3*x+1)

(x^3-2)*(3*x+1)

4*x*(x^3-2)*(3*x+1) = 0

4*x*(x^3-2) = 0

( 4*x )

4*x = 0 // : 4

x = 0

( x^3-2 )

1*x^3 = 2 // : 1

x^3 = 2

x^3 = 2 // ^ 1/3

x = 2^(1/3)

x in { 0, 2^(1/3) }

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