2K(4y-2z)+48y^2+72xy-126z^2-36xz+48y^2-12z^2=0

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Solution for 2K(4y-2z)+48y^2+72xy-126z^2-36xz+48y^2-12z^2=0 equation: 


Simplifying
2K(4y + -2z) + 48y2 + 72xy + -126z2 + -36xz + 48y2 + -12z2 = 0
(4y * 2K + -2z * 2K) + 48y2 + 72xy + -126z2 + -36xz + 48y2 + -12z2 = 0
(8yK + -4zK) + 48y2 + 72xy + -126z2 + -36xz + 48y2 + -12z2 = 0

Reorder the terms:
72xy + -36xz + 8yK + 48y2 + 48y2 + -4zK + -126z2 + -12z2 = 0

Combine like terms: 48y2 + 48y2 = 96y2
72xy + -36xz + 8yK + 96y2 + -4zK + -126z2 + -12z2 = 0

Combine like terms: -126z2 + -12z2 = -138z2
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = 0

Solving
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = 0

Solving for variable 'x'.

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

Add '-8yK' to each side of the equation.
72xy + -36xz + 8yK + 96y2 + -4zK + -8yK + -138z2 = 0 + -8yK

Reorder the terms:
72xy + -36xz + 8yK + -8yK + 96y2 + -4zK + -138z2 = 0 + -8yK

Combine like terms: 8yK + -8yK = 0
72xy + -36xz + 0 + 96y2 + -4zK + -138z2 = 0 + -8yK
72xy + -36xz + 96y2 + -4zK + -138z2 = 0 + -8yK
Remove the zero:
72xy + -36xz + 96y2 + -4zK + -138z2 = -8yK

Add '-96y2' to each side of the equation.
72xy + -36xz + 96y2 + -4zK + -96y2 + -138z2 = -8yK + -96y2

Reorder the terms:
72xy + -36xz + 96y2 + -96y2 + -4zK + -138z2 = -8yK + -96y2

Combine like terms: 96y2 + -96y2 = 0
72xy + -36xz + 0 + -4zK + -138z2 = -8yK + -96y2
72xy + -36xz + -4zK + -138z2 = -8yK + -96y2

Add '4zK' to each side of the equation.
72xy + -36xz + -4zK + 4zK + -138z2 = -8yK + -96y2 + 4zK

Combine like terms: -4zK + 4zK = 0
72xy + -36xz + 0 + -138z2 = -8yK + -96y2 + 4zK
72xy + -36xz + -138z2 = -8yK + -96y2 + 4zK

Add '138z2' to each side of the equation.
72xy + -36xz + -138z2 + 138z2 = -8yK + -96y2 + 4zK + 138z2

Combine like terms: -138z2 + 138z2 = 0
72xy + -36xz + 0 = -8yK + -96y2 + 4zK + 138z2
72xy + -36xz = -8yK + -96y2 + 4zK + 138z2

Reorder the terms:
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = -8yK + 8yK + -96y2 + 96y2 + 4zK + -4zK + 138z2 + -138z2

Combine like terms: -8yK + 8yK = 0
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = 0 + -96y2 + 96y2 + 4zK + -4zK + 138z2 + -138z2
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = -96y2 + 96y2 + 4zK + -4zK + 138z2 + -138z2

Combine like terms: -96y2 + 96y2 = 0
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = 0 + 4zK + -4zK + 138z2 + -138z2
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = 4zK + -4zK + 138z2 + -138z2

Combine like terms: 4zK + -4zK = 0
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = 0 + 138z2 + -138z2
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = 138z2 + -138z2

Combine like terms: 138z2 + -138z2 = 0
72xy + -36xz + 8yK + 96y2 + -4zK + -138z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36xy + -18xz + 4yK + 48y2 + -2zK + -69z2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(36xy + -18xz + 4yK + 48y2 + -2zK + -69z2)' equal to zero and attempt to solve:

Simplifying
36xy + -18xz + 4yK + 48y2 + -2zK + -69z2 = 0

Solving
36xy + -18xz + 4yK + 48y2 + -2zK + -69z2 = 0

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

Add '-4yK' to each side of the equation.
36xy + -18xz + 4yK + 48y2 + -2zK + -4yK + -69z2 = 0 + -4yK

Reorder the terms:
36xy + -18xz + 4yK + -4yK + 48y2 + -2zK + -69z2 = 0 + -4yK

Combine like terms: 4yK + -4yK = 0
36xy + -18xz + 0 + 48y2 + -2zK + -69z2 = 0 + -4yK
36xy + -18xz + 48y2 + -2zK + -69z2 = 0 + -4yK
Remove the zero:
36xy + -18xz + 48y2 + -2zK + -69z2 = -4yK

Add '-48y2' to each side of the equation.
36xy + -18xz + 48y2 + -2zK + -48y2 + -69z2 = -4yK + -48y2

Reorder the terms:
36xy + -18xz + 48y2 + -48y2 + -2zK + -69z2 = -4yK + -48y2

Combine like terms: 48y2 + -48y2 = 0
36xy + -18xz + 0 + -2zK + -69z2 = -4yK + -48y2
36xy + -18xz + -2zK + -69z2 = -4yK + -48y2

Add '2zK' to each side of the equation.
36xy + -18xz + -2zK + 2zK + -69z2 = -4yK + -48y2 + 2zK

Combine like terms: -2zK + 2zK = 0
36xy + -18xz + 0 + -69z2 = -4yK + -48y2 + 2zK
36xy + -18xz + -69z2 = -4yK + -48y2 + 2zK

Add '69z2' to each side of the equation.
36xy + -18xz + -69z2 + 69z2 = -4yK + -48y2 + 2zK + 69z2

Combine like terms: -69z2 + 69z2 = 0
36xy + -18xz + 0 = -4yK + -48y2 + 2zK + 69z2
36xy + -18xz = -4yK + -48y2 + 2zK + 69z2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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