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

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


Simplifying
X + -1y2 + (2zy2 + 2y) * x = z2x + z

Reorder the terms:
X + -1y2 + (2y + 2y2z) * x = z2x + z

Reorder the terms for easier multiplication:
X + -1y2 + x(2y + 2y2z) = z2x + z
X + -1y2 + (2y * x + 2y2z * x) = z2x + z
X + -1y2 + (2xy + 2xy2z) = z2x + z

Reorder the terms:
X + 2xy + 2xy2z + -1y2 = z2x + z

Solving
X + 2xy + 2xy2z + -1y2 = xz2 + z

Solving for variable 'X'.

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

Add '-2xy' to each side of the equation.
X + 2xy + 2xy2z + -2xy + -1y2 = xz2 + -2xy + z

Reorder the terms:
X + 2xy + -2xy + 2xy2z + -1y2 = xz2 + -2xy + z

Combine like terms: 2xy + -2xy = 0
X + 0 + 2xy2z + -1y2 = xz2 + -2xy + z
X + 2xy2z + -1y2 = xz2 + -2xy + z

Reorder the terms:
X + 2xy2z + -1y2 = -2xy + xz2 + z

Add '-2xy2z' to each side of the equation.
X + 2xy2z + -2xy2z + -1y2 = -2xy + xz2 + -2xy2z + z

Combine like terms: 2xy2z + -2xy2z = 0
X + 0 + -1y2 = -2xy + xz2 + -2xy2z + z
X + -1y2 = -2xy + xz2 + -2xy2z + z

Reorder the terms:
X + -1y2 = -2xy + -2xy2z + xz2 + z

Add 'y2' to each side of the equation.
X + -1y2 + y2 = -2xy + -2xy2z + xz2 + y2 + z

Combine like terms: -1y2 + y2 = 0
X + 0 = -2xy + -2xy2z + xz2 + y2 + z
X = -2xy + -2xy2z + xz2 + y2 + z

Simplifying
X = -2xy + -2xy2z + xz2 + y2 + z

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