(3a+9/a^2)*(a^3/6a+18)

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Solution for (3a+9/a^2)*(a^3/6a+18) equation: 


D( a )

a^2 = 0

a^2 = 0

a^2 = 0

1*a^2 = 0 // : 1

a^2 = 0

a = 0

a in (-oo:0) U (0:+oo)

(3*a+9/(a^2))*(a*((a^3)/6)+18) = 0

(3*a+9*a^-2)*(1/6*a^4+18) = 0

3*a+9*a^-2 = 0

3*a*(3*a^-3+1) = 0

3*a^-3 = -1 // : 3

a^-3 = -1/3

-3 < 0

1/(a^3) = -1/3 // * a^3

1 = -1/3*a^3 // : -1/3

-3 = a^3

a^3 = -3 // ^ 1/3

a = -3^(1/3)

3*a*(a+3^(1/3)) = 0

3*a*(a+3^(1/3))*(1/6*a^4+18) = 0

( 1/6*a^4+18 )

1/6*a^4 = -18 // : 1/6

a^4 = -108

( 3*a )

3*a = 0 // : 3

a = 0

( a+3^(1/3) )

a+3^(1/3) = 0 // - 3^(1/3)

a = -3^(1/3)

a in { 0} 

a = -3^(1/3)

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