6x*xy(8x+2y+1)=0

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Solution for 6x*xy(8x+2y+1)=0 equation: 


Simplifying
6x * xy(8x + 2y + 1) = 0

Reorder the terms:
6x * xy(1 + 8x + 2y) = 0

Multiply x * xy
6x2y(1 + 8x + 2y) = 0
(1 * 6x2y + 8x * 6x2y + 2y * 6x2y) = 0

Reorder the terms:
(6x2y + 12x2y2 + 48x3y) = 0
(6x2y + 12x2y2 + 48x3y) = 0

Solving
6x2y + 12x2y2 + 48x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2y'.
6x2y(1 + 2y + 8x) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(1 + 2y + 8x)' equal to zero and attempt to solve:

Simplifying
1 + 2y + 8x = 0

Reorder the terms:
1 + 8x + 2y = 0

Solving
1 + 8x + 2y = 0

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

Add '-1' to each side of the equation.
1 + 8x + -1 + 2y = 0 + -1

Reorder the terms:
1 + -1 + 8x + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8x + 2y = 0 + -1
8x + 2y = 0 + -1

Combine like terms: 0 + -1 = -1
8x + 2y = -1

Add '-2y' to each side of the equation.
8x + 2y + -2y = -1 + -2y

Combine like terms: 2y + -2y = 0
8x + 0 = -1 + -2y
8x = -1 + -2y

Divide each side by '8'.
x = -0.125 + -0.25y

Simplifying
x = -0.125 + -0.25y
Solution
x = {-0.125 + -0.25y}

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