(6xy+2y+6x)(4xy-x)=

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Solution for (6xy+2y+6x)(4xy-x)= equation: 


Simplifying
(6xy + 2y + 6x)(4xy + -1x) = 0

Reorder the terms:
(6x + 6xy + 2y)(4xy + -1x) = 0

Reorder the terms:
(6x + 6xy + 2y)(-1x + 4xy) = 0

Multiply (6x + 6xy + 2y) * (-1x + 4xy)
(6x * (-1x + 4xy) + 6xy * (-1x + 4xy) + 2y * (-1x + 4xy)) = 0
((-1x * 6x + 4xy * 6x) + 6xy * (-1x + 4xy) + 2y * (-1x + 4xy)) = 0
((-6x2 + 24x2y) + 6xy * (-1x + 4xy) + 2y * (-1x + 4xy)) = 0
(-6x2 + 24x2y + (-1x * 6xy + 4xy * 6xy) + 2y * (-1x + 4xy)) = 0
(-6x2 + 24x2y + (-6x2y + 24x2y2) + 2y * (-1x + 4xy)) = 0
(-6x2 + 24x2y + -6x2y + 24x2y2 + (-1x * 2y + 4xy * 2y)) = 0
(-6x2 + 24x2y + -6x2y + 24x2y2 + (-2xy + 8xy2)) = 0

Reorder the terms:
(-2xy + 8xy2 + -6x2 + 24x2y + -6x2y + 24x2y2) = 0

Combine like terms: 24x2y + -6x2y = 18x2y
(-2xy + 8xy2 + -6x2 + 18x2y + 24x2y2) = 0

Solving
-2xy + 8xy2 + -6x2 + 18x2y + 24x2y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1y + 4y2 + -3x + 9xy + 12xy2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1y + 4y2 + -3x + 9xy + 12xy2)' equal to zero and attempt to solve:

Simplifying
-1y + 4y2 + -3x + 9xy + 12xy2 = 0

Reorder the terms:
-3x + 9xy + 12xy2 + -1y + 4y2 = 0

Solving
-3x + 9xy + 12xy2 + -1y + 4y2 = 0

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

Add 'y' to each side of the equation.
-3x + 9xy + 12xy2 + -1y + y + 4y2 = 0 + y

Combine like terms: -1y + y = 0
-3x + 9xy + 12xy2 + 0 + 4y2 = 0 + y
-3x + 9xy + 12xy2 + 4y2 = 0 + y
Remove the zero:
-3x + 9xy + 12xy2 + 4y2 = y

Add '-4y2' to each side of the equation.
-3x + 9xy + 12xy2 + 4y2 + -4y2 = y + -4y2

Combine like terms: 4y2 + -4y2 = 0
-3x + 9xy + 12xy2 + 0 = y + -4y2
-3x + 9xy + 12xy2 = y + -4y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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