0=5x^4-20yx^3+15(y^2)x^2-8(y^3)x+y^4

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Solution for 0=5x^4-20yx^3+15(y^2)x^2-8(y^3)x+y^4 equation: 


Simplifying
0 = 5x4 + -20yx3 + 15(y2) * x2 + -8(y3) * x + y4

Multiply y2 * x2
0 = 5x4 + -20x3y + 15x2y2 + -8(y3) * x + y4

Multiply y3 * x
0 = 5x4 + -20x3y + 15x2y2 + -8xy3 + y4

Reorder the terms:
0 = -8xy3 + 15x2y2 + -20x3y + 5x4 + y4

Solving
0 = -8xy3 + 15x2y2 + -20x3y + 5x4 + y4

Solving for variable 'x'.
Remove the zero:
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = -8xy3 + 15x2y2 + -20x3y + 5x4 + y4 + 8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4

Reorder the terms:
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = -8xy3 + 8xy3 + 15x2y2 + -15x2y2 + -20x3y + 20x3y + 5x4 + -5x4 + y4 + -1y4

Combine like terms: -8xy3 + 8xy3 = 0
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = 0 + 15x2y2 + -15x2y2 + -20x3y + 20x3y + 5x4 + -5x4 + y4 + -1y4
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = 15x2y2 + -15x2y2 + -20x3y + 20x3y + 5x4 + -5x4 + y4 + -1y4

Combine like terms: 15x2y2 + -15x2y2 = 0
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = 0 + -20x3y + 20x3y + 5x4 + -5x4 + y4 + -1y4
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = -20x3y + 20x3y + 5x4 + -5x4 + y4 + -1y4

Combine like terms: -20x3y + 20x3y = 0
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = 0 + 5x4 + -5x4 + y4 + -1y4
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = 5x4 + -5x4 + y4 + -1y4

Combine like terms: 5x4 + -5x4 = 0
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = 0 + y4 + -1y4
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = y4 + -1y4

Combine like terms: y4 + -1y4 = 0
8xy3 + -15x2y2 + 20x3y + -5x4 + -1y4 = 0

The solution to this equation could not be determined.

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