x(8y+10z)=y(8x+8z)andy(8x+8z)

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Solution for x(8y+10z)=y(8x+8z)andy(8x+8z) equation: 


Simplifying
x(8y + 10z) = y(8x + 8z) * andy(8x + 8z)
(8y * x + 10z * x) = y(8x + 8z) * andy(8x + 8z)
(8xy + 10xz) = y(8x + 8z) * andy(8x + 8z)

Reorder the terms for easier multiplication:
8xy + 10xz = y * adny(8x + 8z)(8x + 8z)

Multiply y * adny
8xy + 10xz = adny2(8x + 8z)(8x + 8z)

Multiply (8x + 8z) * (8x + 8z)
8xy + 10xz = adny2(8x * (8x + 8z) + 8z * (8x + 8z))
8xy + 10xz = adny2((8x * 8x + 8z * 8x) + 8z * (8x + 8z))

Reorder the terms:
8xy + 10xz = adny2((64xz + 64x2) + 8z * (8x + 8z))
8xy + 10xz = adny2((64xz + 64x2) + 8z * (8x + 8z))
8xy + 10xz = adny2(64xz + 64x2 + (8x * 8z + 8z * 8z))
8xy + 10xz = adny2(64xz + 64x2 + (64xz + 64z2))

Reorder the terms:
8xy + 10xz = adny2(64xz + 64xz + 64x2 + 64z2)

Combine like terms: 64xz + 64xz = 128xz
8xy + 10xz = adny2(128xz + 64x2 + 64z2)
8xy + 10xz = (128xz * adny2 + 64x2 * adny2 + 64z2 * adny2)
8xy + 10xz = (128adnxy2z + 64adnx2y2 + 64adny2z2)

Solving
8xy + 10xz = 128adnxy2z + 64adnx2y2 + 64adny2z2

Solving for variable 'x'.

Reorder the terms:
-128adnxy2z + -64adnx2y2 + -64adny2z2 + 8xy + 10xz = 128adnxy2z + 64adnx2y2 + 64adny2z2 + -128adnxy2z + -64adnx2y2 + -64adny2z2

Reorder the terms:
-128adnxy2z + -64adnx2y2 + -64adny2z2 + 8xy + 10xz = 128adnxy2z + -128adnxy2z + 64adnx2y2 + -64adnx2y2 + 64adny2z2 + -64adny2z2

Combine like terms: 128adnxy2z + -128adnxy2z = 0
-128adnxy2z + -64adnx2y2 + -64adny2z2 + 8xy + 10xz = 0 + 64adnx2y2 + -64adnx2y2 + 64adny2z2 + -64adny2z2
-128adnxy2z + -64adnx2y2 + -64adny2z2 + 8xy + 10xz = 64adnx2y2 + -64adnx2y2 + 64adny2z2 + -64adny2z2

Combine like terms: 64adnx2y2 + -64adnx2y2 = 0
-128adnxy2z + -64adnx2y2 + -64adny2z2 + 8xy + 10xz = 0 + 64adny2z2 + -64adny2z2
-128adnxy2z + -64adnx2y2 + -64adny2z2 + 8xy + 10xz = 64adny2z2 + -64adny2z2

Combine like terms: 64adny2z2 + -64adny2z2 = 0
-128adnxy2z + -64adnx2y2 + -64adny2z2 + 8xy + 10xz = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-64adnxy2z + -32adnx2y2 + -32adny2z2 + 4xy + 5xz) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-64adnxy2z + -32adnx2y2 + -32adny2z2 + 4xy + 5xz)' equal to zero and attempt to solve:

Simplifying
-64adnxy2z + -32adnx2y2 + -32adny2z2 + 4xy + 5xz = 0

Solving
-64adnxy2z + -32adnx2y2 + -32adny2z2 + 4xy + 5xz = 0

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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