X^2+2Y^2+2ZY+2Z^2=1

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Solution for X^2+2Y^2+2ZY+2Z^2=1 equation: 


Simplifying
X2 + 2Y2 + 2ZY + 2Z2 = 1

Reorder the terms:
X2 + 2YZ + 2Y2 + 2Z2 = 1

Solving
X2 + 2YZ + 2Y2 + 2Z2 = 1

Solving for variable 'X'.

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

Add '-2YZ' to each side of the equation.
X2 + 2YZ + 2Y2 + -2YZ + 2Z2 = 1 + -2YZ

Reorder the terms:
X2 + 2YZ + -2YZ + 2Y2 + 2Z2 = 1 + -2YZ

Combine like terms: 2YZ + -2YZ = 0
X2 + 0 + 2Y2 + 2Z2 = 1 + -2YZ
X2 + 2Y2 + 2Z2 = 1 + -2YZ

Add '-2Y2' to each side of the equation.
X2 + 2Y2 + -2Y2 + 2Z2 = 1 + -2YZ + -2Y2

Combine like terms: 2Y2 + -2Y2 = 0
X2 + 0 + 2Z2 = 1 + -2YZ + -2Y2
X2 + 2Z2 = 1 + -2YZ + -2Y2

Add '-2Z2' to each side of the equation.
X2 + 2Z2 + -2Z2 = 1 + -2YZ + -2Y2 + -2Z2

Combine like terms: 2Z2 + -2Z2 = 0
X2 + 0 = 1 + -2YZ + -2Y2 + -2Z2
X2 = 1 + -2YZ + -2Y2 + -2Z2

Simplifying
X2 = 1 + -2YZ + -2Y2 + -2Z2

Reorder the terms:
-1 + X2 + 2YZ + 2Y2 + 2Z2 = 1 + -2YZ + -2Y2 + -2Z2 + -1 + 2YZ + 2Y2 + 2Z2

Reorder the terms:
-1 + X2 + 2YZ + 2Y2 + 2Z2 = 1 + -1 + -2YZ + 2YZ + -2Y2 + 2Y2 + -2Z2 + 2Z2

Combine like terms: 1 + -1 = 0
-1 + X2 + 2YZ + 2Y2 + 2Z2 = 0 + -2YZ + 2YZ + -2Y2 + 2Y2 + -2Z2 + 2Z2
-1 + X2 + 2YZ + 2Y2 + 2Z2 = -2YZ + 2YZ + -2Y2 + 2Y2 + -2Z2 + 2Z2

Combine like terms: -2YZ + 2YZ = 0
-1 + X2 + 2YZ + 2Y2 + 2Z2 = 0 + -2Y2 + 2Y2 + -2Z2 + 2Z2
-1 + X2 + 2YZ + 2Y2 + 2Z2 = -2Y2 + 2Y2 + -2Z2 + 2Z2

Combine like terms: -2Y2 + 2Y2 = 0
-1 + X2 + 2YZ + 2Y2 + 2Z2 = 0 + -2Z2 + 2Z2
-1 + X2 + 2YZ + 2Y2 + 2Z2 = -2Z2 + 2Z2

Combine like terms: -2Z2 + 2Z2 = 0
-1 + X2 + 2YZ + 2Y2 + 2Z2 = 0

The solution to this equation could not be determined.

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