(X+y+2z)(x+y-2z)=0

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Solution for (X+y+2z)(x+y-2z)=0 equation: 


Simplifying
(X + y + 2z)(x + y + -2z) = 0

Multiply (X + y + 2z) * (x + y + -2z)
(X(x + y + -2z) + y(x + y + -2z) + 2z * (x + y + -2z)) = 0
((x * X + y * X + -2z * X) + y(x + y + -2z) + 2z * (x + y + -2z)) = 0
((xX + yX + -2zX) + y(x + y + -2z) + 2z * (x + y + -2z)) = 0
(xX + yX + -2zX + (x * y + y * y + -2z * y) + 2z * (x + y + -2z)) = 0

Reorder the terms:
(xX + yX + -2zX + (xy + -2yz + y2) + 2z * (x + y + -2z)) = 0
(xX + yX + -2zX + (xy + -2yz + y2) + 2z * (x + y + -2z)) = 0
(xX + yX + -2zX + xy + -2yz + y2 + (x * 2z + y * 2z + -2z * 2z)) = 0
(xX + yX + -2zX + xy + -2yz + y2 + (2xz + 2yz + -4z2)) = 0

Reorder the terms:
(xX + xy + 2xz + yX + -2yz + 2yz + y2 + -2zX + -4z2) = 0

Combine like terms: -2yz + 2yz = 0
(xX + xy + 2xz + yX + 0 + y2 + -2zX + -4z2) = 0
(xX + xy + 2xz + yX + y2 + -2zX + -4z2) = 0

Solving
xX + xy + 2xz + yX + y2 + -2zX + -4z2 = 0

Solving for variable 'x'.

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

Add '-1yX' to each side of the equation.
xX + xy + 2xz + yX + y2 + -2zX + -1yX + -4z2 = 0 + -1yX

Reorder the terms:
xX + xy + 2xz + yX + -1yX + y2 + -2zX + -4z2 = 0 + -1yX

Combine like terms: yX + -1yX = 0
xX + xy + 2xz + 0 + y2 + -2zX + -4z2 = 0 + -1yX
xX + xy + 2xz + y2 + -2zX + -4z2 = 0 + -1yX
Remove the zero:
xX + xy + 2xz + y2 + -2zX + -4z2 = -1yX

Add '-1y2' to each side of the equation.
xX + xy + 2xz + y2 + -2zX + -1y2 + -4z2 = -1yX + -1y2

Reorder the terms:
xX + xy + 2xz + y2 + -1y2 + -2zX + -4z2 = -1yX + -1y2

Combine like terms: y2 + -1y2 = 0
xX + xy + 2xz + 0 + -2zX + -4z2 = -1yX + -1y2
xX + xy + 2xz + -2zX + -4z2 = -1yX + -1y2

Add '2zX' to each side of the equation.
xX + xy + 2xz + -2zX + 2zX + -4z2 = -1yX + -1y2 + 2zX

Combine like terms: -2zX + 2zX = 0
xX + xy + 2xz + 0 + -4z2 = -1yX + -1y2 + 2zX
xX + xy + 2xz + -4z2 = -1yX + -1y2 + 2zX

Add '4z2' to each side of the equation.
xX + xy + 2xz + -4z2 + 4z2 = -1yX + -1y2 + 2zX + 4z2

Combine like terms: -4z2 + 4z2 = 0
xX + xy + 2xz + 0 = -1yX + -1y2 + 2zX + 4z2
xX + xy + 2xz = -1yX + -1y2 + 2zX + 4z2

Reorder the terms:
xX + xy + 2xz + yX + y2 + -2zX + -4z2 = -1yX + yX + -1y2 + y2 + 2zX + -2zX + 4z2 + -4z2

Combine like terms: -1yX + yX = 0
xX + xy + 2xz + yX + y2 + -2zX + -4z2 = 0 + -1y2 + y2 + 2zX + -2zX + 4z2 + -4z2
xX + xy + 2xz + yX + y2 + -2zX + -4z2 = -1y2 + y2 + 2zX + -2zX + 4z2 + -4z2

Combine like terms: -1y2 + y2 = 0
xX + xy + 2xz + yX + y2 + -2zX + -4z2 = 0 + 2zX + -2zX + 4z2 + -4z2
xX + xy + 2xz + yX + y2 + -2zX + -4z2 = 2zX + -2zX + 4z2 + -4z2

Combine like terms: 2zX + -2zX = 0
xX + xy + 2xz + yX + y2 + -2zX + -4z2 = 0 + 4z2 + -4z2
xX + xy + 2xz + yX + y2 + -2zX + -4z2 = 4z2 + -4z2

Combine like terms: 4z2 + -4z2 = 0
xX + xy + 2xz + yX + y2 + -2zX + -4z2 = 0

The solution to this equation could not be determined.

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