((4x-1)^2(4x^2-25)/(4x-1)(2x^2-3x-5))

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Solution for ((4x-1)^2(4x^2-25)/(4x-1)(2x^2-3x-5)) equation: 


D( x )

4*x-1 = 0

4*x-1 = 0

4*x-1 = 0

4*x-1 = 0 // + 1

4*x = 1 // : 4

x = 1/4

x in (-oo:1/4) U (1/4:+oo)

(((4*x-1)^2*(4*x^2-25))/(4*x-1))*(2*x^2-(3*x)-5) = 0

(((4*x-1)^2*(4*x^2-25))/(4*x-1))*(2*x^2-3*x-5) = 0

(4*x-1)*(4*x^2-25)*(2*x^2-3*x-5) = 0

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

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

DELTA = (-3)^2-(-5*2*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+3)/(2*2) or x = (3-49^(1/2))/(2*2)

x = 5/2 or x = -1

(x+1)*(x-5/2) = 0

(4*x-1)*(4*x^2-25)*(x+1)*(x-5/2) = 0

( 4*x-1 )

4*x-1 = 0 // + 1

4*x = 1 // : 4

x = 1/4

( 4*x^2-25 )

4*x^2 = 25 // : 4

x^2 = 25/4

x^2 = 25/4 // ^ 1/2

abs(x) = 5/2

x = 5/2 or x = -5/2

( x+1 )

x+1 = 0 // - 1

x = -1

( x-5/2 )

x-5/2 = 0 // + 5/2

x = 5/2

x in { 1/4} 

x in { 5/2, -5/2, -1, 5/2 }

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