x-y^2+(2zy^2+2y)x=z^2+z

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Solution for x-y^2+(2zy^2+2y)x=z^2+z equation:


Simplifying
x + -1y2 + (2zy2 + 2y) * x = z2 + z

Reorder the terms:
x + -1y2 + (2y + 2y2z) * x = z2 + z

Reorder the terms for easier multiplication:
x + -1y2 + x(2y + 2y2z) = z2 + z
x + -1y2 + (2y * x + 2y2z * x) = z2 + z
x + -1y2 + (2xy + 2xy2z) = z2 + z

Reorder the terms:
x + 2xy + 2xy2z + -1y2 = z2 + z

Reorder the terms:
x + 2xy + 2xy2z + -1y2 = z + z2

Solving
x + 2xy + 2xy2z + -1y2 = z + z2

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add 'y2' to each side of the equation.
x + 2xy + 2xy2z + -1y2 + y2 = z + y2 + z2

Combine like terms: -1y2 + y2 = 0
x + 2xy + 2xy2z + 0 = z + y2 + z2
x + 2xy + 2xy2z = z + y2 + z2

Reorder the terms:
x + 2xy + 2xy2z = y2 + z + z2

Reorder the terms:
x + 2xy + 2xy2z + -1y2 + -1z + -1z2 = y2 + -1y2 + z + -1z + z2 + -1z2

Combine like terms: y2 + -1y2 = 0
x + 2xy + 2xy2z + -1y2 + -1z + -1z2 = 0 + z + -1z + z2 + -1z2
x + 2xy + 2xy2z + -1y2 + -1z + -1z2 = z + -1z + z2 + -1z2

Combine like terms: z + -1z = 0
x + 2xy + 2xy2z + -1y2 + -1z + -1z2 = 0 + z2 + -1z2
x + 2xy + 2xy2z + -1y2 + -1z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
x + 2xy + 2xy2z + -1y2 + -1z + -1z2 = 0

The solution to this equation could not be determined.

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