((x^2-2x-24)/(4x^3-5x^2))*((x^3-x^2)/(2x-12))

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Solution for ((x^2-2x-24)/(4x^3-5x^2))*((x^3-x^2)/(2x-12)) equation: 


D( x )

4*x^3-(5*x^2) = 0

2*x-12 = 0

4*x^3-(5*x^2) = 0

4*x^3-(5*x^2) = 0

4*x^3-5*x^2 = 0

4*x^3-5*x^2 = 0

x^2*(4*x-5) = 0

4*x-5 = 0 // + 5

4*x = 5 // : 4

x = 5/4

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

2*x-12 = 0

2*x-12 = 0

2*x-12 = 0 // + 12

2*x = 12 // : 2

x = 12/2

x = 6

x in (-oo:0) U (0:5/4) U (5/4:6) U (6:+oo)

((x^2-(2*x)-24)/(4*x^3-(5*x^2)))*((x^3-x^2)/(2*x-12)) = 0

((x^2-2*x-24)/(4*x^3-5*x^2))*((x^3-x^2)/(2*x-12)) = 0

((x^2-2*x-24)*(x^3-x^2))/((4*x^3-5*x^2)*(2*x-12)) = 0

x^2-2*x-24 = 0

x^2-2*x-24 = 0

DELTA = (-2)^2-(-24*1*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)+2)/(1*2) or x = (2-100^(1/2))/(1*2)

x = 6 or x = -4

(x+4)*(x-6) = 0

4*x^3-5*x^2 = 0

x^2*(4*x-5) = 0

4*x-5 = 0 // + 5

4*x = 5 // : 4

x = 5/4

x^2*(x-5/4) = 0

x^3-x^2 = 0

x^2*(x-1) = 0

x-1 = 0 // + 1

x = 1

x^2*(x-1) = 0

(x^2*(x+4)*(x-6)*(x-1))/(x^2*(x-5/4)*(2*x-12)) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-1 )

x-1 = 0 // + 1

x = 1

( x-6 )

x-6 = 0 // + 6

x = 6

( x^2 )

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { 6} 

x in { 0} 

x in { -4, 1 }

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