(8xy+6)(x+y)(x-y)=0

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Solution for (8xy+6)(x+y)(x-y)=0 equation: 


Simplifying
(8xy + 6)(x + y)(x + -1y) = 0

Reorder the terms:
(6 + 8xy)(x + y)(x + -1y) = 0

Multiply (6 + 8xy) * (x + y)
(6(x + y) + 8xy * (x + y))(x + -1y) = 0
((x * 6 + y * 6) + 8xy * (x + y))(x + -1y) = 0
((6x + 6y) + 8xy * (x + y))(x + -1y) = 0
(6x + 6y + (x * 8xy + y * 8xy))(x + -1y) = 0

Reorder the terms:
(6x + 6y + (8xy2 + 8x2y))(x + -1y) = 0
(6x + 6y + (8xy2 + 8x2y))(x + -1y) = 0

Reorder the terms:
(6x + 8xy2 + 8x2y + 6y)(x + -1y) = 0
(6x + 8xy2 + 8x2y + 6y)(x + -1y) = 0

Multiply (6x + 8xy2 + 8x2y + 6y) * (x + -1y)
(6x * (x + -1y) + 8xy2 * (x + -1y) + 8x2y * (x + -1y) + 6y * (x + -1y)) = 0
((x * 6x + -1y * 6x) + 8xy2 * (x + -1y) + 8x2y * (x + -1y) + 6y * (x + -1y)) = 0

Reorder the terms:
((-6xy + 6x2) + 8xy2 * (x + -1y) + 8x2y * (x + -1y) + 6y * (x + -1y)) = 0
((-6xy + 6x2) + 8xy2 * (x + -1y) + 8x2y * (x + -1y) + 6y * (x + -1y)) = 0
(-6xy + 6x2 + (x * 8xy2 + -1y * 8xy2) + 8x2y * (x + -1y) + 6y * (x + -1y)) = 0

Reorder the terms:
(-6xy + 6x2 + (-8xy3 + 8x2y2) + 8x2y * (x + -1y) + 6y * (x + -1y)) = 0
(-6xy + 6x2 + (-8xy3 + 8x2y2) + 8x2y * (x + -1y) + 6y * (x + -1y)) = 0
(-6xy + 6x2 + -8xy3 + 8x2y2 + (x * 8x2y + -1y * 8x2y) + 6y * (x + -1y)) = 0

Reorder the terms:
(-6xy + 6x2 + -8xy3 + 8x2y2 + (-8x2y2 + 8x3y) + 6y * (x + -1y)) = 0
(-6xy + 6x2 + -8xy3 + 8x2y2 + (-8x2y2 + 8x3y) + 6y * (x + -1y)) = 0
(-6xy + 6x2 + -8xy3 + 8x2y2 + -8x2y2 + 8x3y + (x * 6y + -1y * 6y)) = 0
(-6xy + 6x2 + -8xy3 + 8x2y2 + -8x2y2 + 8x3y + (6xy + -6y2)) = 0

Reorder the terms:
(-6xy + 6xy + -8xy3 + 6x2 + 8x2y2 + -8x2y2 + 8x3y + -6y2) = 0

Combine like terms: -6xy + 6xy = 0
(0 + -8xy3 + 6x2 + 8x2y2 + -8x2y2 + 8x3y + -6y2) = 0
(-8xy3 + 6x2 + 8x2y2 + -8x2y2 + 8x3y + -6y2) = 0

Combine like terms: 8x2y2 + -8x2y2 = 0
(-8xy3 + 6x2 + 0 + 8x3y + -6y2) = 0
(-8xy3 + 6x2 + 8x3y + -6y2) = 0

Solving
-8xy3 + 6x2 + 8x3y + -6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4xy3 + 3x2 + 4x3y + -3y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4xy3 + 3x2 + 4x3y + -3y2)' equal to zero and attempt to solve:

Simplifying
-4xy3 + 3x2 + 4x3y + -3y2 = 0

Solving
-4xy3 + 3x2 + 4x3y + -3y2 = 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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