1-12/(3z-3)=-20/(3z-3)^2

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Solution for 1-12/(3z-3)=-20/(3z-3)^2 equation: 


D( z )

(3*z-3)^2 = 0

3*z-3 = 0

(3*z-3)^2 = 0

(3*z-3)^2 = 0

3*z-3 = 0 // + 3

3*z = 3 // : 3

z = 3/3

z = 1

3*z-3 = 0

3*z-3 = 0

3*z-3 = 0 // + 3

3*z = 3 // : 3

z = 3/3

z = 1

z in (-oo:1) U (1:+oo)

1-(12/(3*z-3)) = -20/((3*z-3)^2) // + -20/((3*z-3)^2)

1-(12/(3*z-3))-(-20/((3*z-3)^2)) = 0

20*(3*z-3)^-2-12*(3*z-3)^-1+1 = 0

20/((3*z-3)^2)-12/(3*z-3)+1 = 0

(-12*(3*z-3))/((3*z-3)^2)+20/((3*z-3)^2)+(1*(3*z-3)^2)/((3*z-3)^2) = 0

1*(3*z-3)^2-12*(3*z-3)+20 = 0

9*z^2-36*z-18*z+9+56 = 0

9*z^2-54*z+65 = 0

9*z^2-54*z+65 = 0

9*z^2-54*z+65 = 0

DELTA = (-54)^2-(4*9*65)

DELTA = 576

DELTA > 0

z = (576^(1/2)+54)/(2*9) or z = (54-576^(1/2))/(2*9)

z = 13/3 or z = 5/3

(z-5/3)*(z-13/3) = 0

((z-5/3)*(z-13/3))/((3*z-3)^2) = 0

((z-5/3)*(z-13/3))/((3*z-3)^2) = 0 // * (3*z-3)^2

(z-5/3)*(z-13/3) = 0

( z-13/3 )

z-13/3 = 0 // + 13/3

z = 13/3

( z-5/3 )

z-5/3 = 0 // + 5/3

z = 5/3

z in { 13/3, 5/3 }

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