(4z^6-6z^4)/(2z^3)

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Solution for (4z^6-6z^4)/(2z^3) equation: 


D( z )

2*z^3 = 0

2*z^3 = 0

2*z^3 = 0

2*z^3 = 0 // : 2

z^3 = 0

z = 0

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

(4*z^6-(6*z^4))/(2*z^3) = 0

(4*z^6-6*z^4)/(2*z^3) = 0

4*z^6-6*z^4 = 0

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

2*z^2 = 3 // : 2

z^2 = 3/2

z^2 = 3/2 // ^ 1/2

abs(z) = (3/2)^(1/2)

z = (3/2)^(1/2) or z = -(3/2)^(1/2)

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

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

( 2*z^4 )

2*z^4 = 0 // : 2

z^4 = 0

z = 0

( z+(3/2)^(1/2) )

z+(3/2)^(1/2) = 0 // - (3/2)^(1/2)

z = -(3/2)^(1/2)

( z-(3/2)^(1/2) )

z-(3/2)^(1/2) = 0 // + (3/2)^(1/2)

z = (3/2)^(1/2)

z in { 0} 

z in { -(3/2)^(1/2), (3/2)^(1/2) }

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