2x+3=4xy+4x+2y+4x^2+3

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Solution for 2x+3=4xy+4x+2y+4x^2+3 equation: 


Simplifying
2x + 3 = 4xy + 4x + 2y + 4x2 + 3

Reorder the terms:
3 + 2x = 4xy + 4x + 2y + 4x2 + 3

Reorder the terms:
3 + 2x = 3 + 4x + 4xy + 4x2 + 2y

Add '-3' to each side of the equation.
3 + -3 + 2x = 3 + 4x + 4xy + 4x2 + -3 + 2y

Combine like terms: 3 + -3 = 0
0 + 2x = 3 + 4x + 4xy + 4x2 + -3 + 2y
2x = 3 + 4x + 4xy + 4x2 + -3 + 2y

Reorder the terms:
2x = 3 + -3 + 4x + 4xy + 4x2 + 2y

Combine like terms: 3 + -3 = 0
2x = 0 + 4x + 4xy + 4x2 + 2y
2x = 4x + 4xy + 4x2 + 2y

Solving
2x = 4x + 4xy + 4x2 + 2y

Solving for variable 'x'.

Combine like terms: 2x + -4x = -2x
-2x + -4xy + -4x2 + -2y = 4x + 4xy + 4x2 + 2y + -4x + -4xy + -4x2 + -2y

Reorder the terms:
-2x + -4xy + -4x2 + -2y = 4x + -4x + 4xy + -4xy + 4x2 + -4x2 + 2y + -2y

Combine like terms: 4x + -4x = 0
-2x + -4xy + -4x2 + -2y = 0 + 4xy + -4xy + 4x2 + -4x2 + 2y + -2y
-2x + -4xy + -4x2 + -2y = 4xy + -4xy + 4x2 + -4x2 + 2y + -2y

Combine like terms: 4xy + -4xy = 0
-2x + -4xy + -4x2 + -2y = 0 + 4x2 + -4x2 + 2y + -2y
-2x + -4xy + -4x2 + -2y = 4x2 + -4x2 + 2y + -2y

Combine like terms: 4x2 + -4x2 = 0
-2x + -4xy + -4x2 + -2y = 0 + 2y + -2y
-2x + -4xy + -4x2 + -2y = 2y + -2y

Combine like terms: 2y + -2y = 0
-2x + -4xy + -4x2 + -2y = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(x + 2xy + 2x2 + y) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(x + 2xy + 2x2 + y)' equal to zero and attempt to solve:

Simplifying
x + 2xy + 2x2 + y = 0

Solving
x + 2xy + 2x2 + y = 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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