(3z^(1/6))(5z^(5/6)-2z^12)

Solution for (3z^(1/6))(5z^(5/6)-2z^12) equation:

D( z )

z < 0

z < 0

z in <0:+oo)

3*z^(1/6)*(5*z^(5/6)-(2*z^12)) = 0

3*z^(1/6)*(5*z^(5/6)-2*z^12) = 0

5*z^(5/6)-2*z^12 = 0

z^(5/6)*(5-2*z^(67/6)) = 0

-2*z^(67/6) = -5 // : -2

z^(67/6) = 5/2

z^(67/6) = 5/2 // ^ 6

z^67 = 15625/64 // ^ 1/67

z = (15625/64)^(1/67)

z^(5/6)*(z-(15625/64)^(1/67)) = 0

3*z^(1/6)*z^(5/6)*(z-(15625/64)^(1/67)) = 0

( 3*z^(1/6) )

3*z^(1/6) = 0 // : 3

z^(1/6) = 0

z = 0

( z-(15625/64)^(1/67) )

z-(15625/64)^(1/67) = 0 // + (15625/64)^(1/67)

z = (15625/64)^(1/67)

( z^(5/6) )

1*z^(5/6) = 0 // : 1

z^(5/6) = 0

z = 0

z in { 0, (15625/64)^(1/67), 0 }