2x=2xln(2x+1)

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Solution for 2x=2xln(2x+1) equation: 


Simplifying
2x = 2xln(2x + 1)

Reorder the terms:
2x = 2lnx(1 + 2x)
2x = (1 * 2lnx + 2x * 2lnx)
2x = (2lnx + 4lnx2)

Solving
2x = 2lnx + 4lnx2

Solving for variable 'x'.

Reorder the terms:
-2lnx + -4lnx2 + 2x = 2lnx + 4lnx2 + -2lnx + -4lnx2

Reorder the terms:
-2lnx + -4lnx2 + 2x = 2lnx + -2lnx + 4lnx2 + -4lnx2

Combine like terms: 2lnx + -2lnx = 0
-2lnx + -4lnx2 + 2x = 0 + 4lnx2 + -4lnx2
-2lnx + -4lnx2 + 2x = 4lnx2 + -4lnx2

Combine like terms: 4lnx2 + -4lnx2 = 0
-2lnx + -4lnx2 + 2x = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1ln + -2lnx + 1) = 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 '(-1ln + -2lnx + 1)' equal to zero and attempt to solve:

Simplifying
-1ln + -2lnx + 1 = 0

Reorder the terms:
1 + -1ln + -2lnx = 0

Solving
1 + -1ln + -2lnx = 0

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

Add '-1' to each side of the equation.
1 + -1ln + -1 + -2lnx = 0 + -1

Reorder the terms:
1 + -1 + -1ln + -2lnx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1ln + -2lnx = 0 + -1
-1ln + -2lnx = 0 + -1

Combine like terms: 0 + -1 = -1
-1ln + -2lnx = -1

Add 'ln' to each side of the equation.
-1ln + ln + -2lnx = -1 + ln

Combine like terms: -1ln + ln = 0
0 + -2lnx = -1 + ln
-2lnx = -1 + ln

Divide each side by '-2ln'.
x = 0.5l-1n-1 + -0.5

Simplifying
x = 0.5l-1n-1 + -0.5

Reorder the terms:
x = -0.5 + 0.5l-1n-1
Solution
x = {0, -0.5 + 0.5l-1n-1}

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