(1/(z+6))-(4/z)=(2z+6)/(z^2+6z)

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Solution for (1/(z+6))-(4/z)=(2z+6)/(z^2+6z) equation: 


D( z )

z+6 = 0

z = 0

z^2+6*z = 0

z+6 = 0

z+6 = 0

z+6 = 0 // - 6

z = -6

z = 0

z = 0

z^2+6*z = 0

z^2+6*z = 0

z^2+6*z = 0

DELTA = 6^2-(0*1*4)

DELTA = 36

DELTA > 0

z = (36^(1/2)-6)/(1*2) or z = (-36^(1/2)-6)/(1*2)

z = 0 or z = -6

z in (-oo:-6) U (-6:0) U (0:+oo)

1/(z+6)-(4/z) = (2*z+6)/(z^2+6*z) // - (2*z+6)/(z^2+6*z)

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

1/(z+6)-((2*z+6)/(z^2+6*z))-4*z^-1 = 0

1/(z+6)+(-1*(2*z+6))/(z^2+6*z)-4/z = 0

z^2+6*z = 0

z^2+6*z = 0

z*(z+6) = 0

z+6 = 0 // - 6

z = -6

z*(z+6) = 0

1/(z+6)+(-1*(2*z+6))/(z*(z+6))-4/z = 0

(1*z)/(z*(z+6))+(-1*(2*z+6))/(z*(z+6))+(-4*(z+6))/(z*(z+6)) = 0

1*z-1*(2*z+6)-4*(z+6) = 0

-z-4*z-24-6 = 0

-5*z-30 = 0

(-5*z-30)/(z*(z+6)) = 0

(-5*z-30)/(z*(z+6)) = 0 // * z*(z+6)

-5*z-30 = 0

-5*z-30 = 0 // + 30

-5*z = 30 // : -5

z = 30/(-5)

z = -6

z in { -6} 

z belongs to the empty set

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