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

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


Simplifying
(2x + y + -2z)(2x + -1y + 2z) = 0

Multiply (2x + y + -2z) * (2x + -1y + 2z)
(2x * (2x + -1y + 2z) + y(2x + -1y + 2z) + -2z * (2x + -1y + 2z)) = 0
((2x * 2x + -1y * 2x + 2z * 2x) + y(2x + -1y + 2z) + -2z * (2x + -1y + 2z)) = 0

Reorder the terms:
((-2xy + 4xz + 4x2) + y(2x + -1y + 2z) + -2z * (2x + -1y + 2z)) = 0
((-2xy + 4xz + 4x2) + y(2x + -1y + 2z) + -2z * (2x + -1y + 2z)) = 0
(-2xy + 4xz + 4x2 + (2x * y + -1y * y + 2z * y) + -2z * (2x + -1y + 2z)) = 0

Reorder the terms:
(-2xy + 4xz + 4x2 + (2xy + 2yz + -1y2) + -2z * (2x + -1y + 2z)) = 0
(-2xy + 4xz + 4x2 + (2xy + 2yz + -1y2) + -2z * (2x + -1y + 2z)) = 0
(-2xy + 4xz + 4x2 + 2xy + 2yz + -1y2 + (2x * -2z + -1y * -2z + 2z * -2z)) = 0
(-2xy + 4xz + 4x2 + 2xy + 2yz + -1y2 + (-4xz + 2yz + -4z2)) = 0

Reorder the terms:
(-2xy + 2xy + 4xz + -4xz + 4x2 + 2yz + 2yz + -1y2 + -4z2) = 0

Combine like terms: -2xy + 2xy = 0
(0 + 4xz + -4xz + 4x2 + 2yz + 2yz + -1y2 + -4z2) = 0
(4xz + -4xz + 4x2 + 2yz + 2yz + -1y2 + -4z2) = 0

Combine like terms: 4xz + -4xz = 0
(0 + 4x2 + 2yz + 2yz + -1y2 + -4z2) = 0
(4x2 + 2yz + 2yz + -1y2 + -4z2) = 0

Combine like terms: 2yz + 2yz = 4yz
(4x2 + 4yz + -1y2 + -4z2) = 0

Solving
4x2 + 4yz + -1y2 + -4z2 = 0

Solving for variable 'x'.

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

Add '-4yz' to each side of the equation.
4x2 + 4yz + -1y2 + -4yz + -4z2 = 0 + -4yz

Reorder the terms:
4x2 + 4yz + -4yz + -1y2 + -4z2 = 0 + -4yz

Combine like terms: 4yz + -4yz = 0
4x2 + 0 + -1y2 + -4z2 = 0 + -4yz
4x2 + -1y2 + -4z2 = 0 + -4yz
Remove the zero:
4x2 + -1y2 + -4z2 = -4yz

Add 'y2' to each side of the equation.
4x2 + -1y2 + y2 + -4z2 = -4yz + y2

Combine like terms: -1y2 + y2 = 0
4x2 + 0 + -4z2 = -4yz + y2
4x2 + -4z2 = -4yz + y2

Add '4z2' to each side of the equation.
4x2 + -4z2 + 4z2 = -4yz + y2 + 4z2

Combine like terms: -4z2 + 4z2 = 0
4x2 + 0 = -4yz + y2 + 4z2
4x2 = -4yz + y2 + 4z2

Divide each side by '4'.
x2 = -1yz + 0.25y2 + z2

Simplifying
x2 = -1yz + 0.25y2 + z2

Reorder the terms:
x2 + yz + -0.25y2 + -1z2 = -1yz + yz + 0.25y2 + -0.25y2 + z2 + -1z2

Combine like terms: -1yz + yz = 0
x2 + yz + -0.25y2 + -1z2 = 0 + 0.25y2 + -0.25y2 + z2 + -1z2
x2 + yz + -0.25y2 + -1z2 = 0.25y2 + -0.25y2 + z2 + -1z2

Combine like terms: 0.25y2 + -0.25y2 = 0.00
x2 + yz + -0.25y2 + -1z2 = 0.00 + z2 + -1z2
x2 + yz + -0.25y2 + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
x2 + yz + -0.25y2 + -1z2 = 0

The solution to this equation could not be determined.

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