(10x^4y^3+5x^3y^2-25x^2y^4)/-5x^2y

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Solution for (10x^4y^3+5x^3y^2-25x^2y^4)/-5x^2y equation: 


x in (-oo:+oo)

x^2*y*((10*x^4*y^3-(25*x^2*y^4)+5*x^3*y^2)/(-5)) = 0

x^2*y*((10*x^4*y^3-25*x^2*y^4+5*x^3*y^2)/(-5)) = 0

(x^2*y*(10*x^4*y^3-25*x^2*y^4+5*x^3*y^2))/(-5) = 0

( 10*x^4*y^3-25*x^2*y^4+5*x^3*y^2 )

10*x^4*y^3-25*x^2*y^4+5*x^3*y^2 = 0

5*x^2*y^2*(x-5*y^2+2*x^2*y) = 0

x+2*x^2*y-5*y^2 = 0

DELTA = 1^2-(-5*2*4*y*y^2)

DELTA = 40*y^3+1

40*y^3+1 = 0

40*y^3 = -1 // : 40

y^3 = -1/40

y^3 = -1/40 // ^ 1/3

y = -(1/40)^(1/3)

DELTA = 0  <=>  t_2 = -(1/40)^(1/3)

x = -1/(2*2*y) i y = -(1/40)^(1/3)

x = -1/(4*y) i y = -(1/40)^(1/3)

( x = ((40*y^3+1)^(1/2)-1)/(2*2*y) or x = (-(40*y^3+1)^(1/2)-1)/(2*2*y) ) i y > -(1/40)^(1/3)

( x = ((40*y^3+1)^(1/2)-1)/(4*y) or x = (-1/4)*y^-1*((40*y^3+1)^(1/2)+1) ) i y > -(1/40)^(1/3)

y+(1/40)^(1/3) > 0

y+(1/40)^(1/3) > 0 // - (1/40)^(1/3)

y > -(1/40)^(1/3)

5*x^2*y^2 = 0

5*x^2*y^2 = 0 // : 5*y^2

x^2 = 0

x = 0

( x^2*y )

x^2*y = 0 // : y

x^2 = 0

x = 0

x in { -1/(4*y), ((40*y^3+1)^(1/2)-1)/(4*y), (-1/4)*y^-1*((40*y^3+1)^(1/2)+1), 0, 0 }

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