2lnx=ln(2(a+1)x-a^2-2a)

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Solution for 2lnx=ln(2(a+1)x-a^2-2a) equation: 


Simplifying
2lnx = ln(2(a + 1) * x + -1a2 + -2a)

Reorder the terms:
2lnx = ln(2(1 + a) * x + -1a2 + -2a)

Reorder the terms for easier multiplication:
2lnx = ln(2x(1 + a) + -1a2 + -2a)
2lnx = ln((1 * 2x + a * 2x) + -1a2 + -2a)

Reorder the terms:
2lnx = ln((2ax + 2x) + -1a2 + -2a)
2lnx = ln((2ax + 2x) + -1a2 + -2a)

Reorder the terms:
2lnx = ln(-2a + 2ax + -1a2 + 2x)
2lnx = (-2a * ln + 2ax * ln + -1a2 * ln + 2x * ln)
2lnx = (-2aln + 2alnx + -1a2ln + 2lnx)

Add '-2lnx' to each side of the equation.
2lnx + -2lnx = -2aln + 2alnx + -1a2ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
0 = -2aln + 2alnx + -1a2ln + 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
0 = -2aln + 2alnx + -1a2ln + 0
0 = -2aln + 2alnx + -1a2ln

Solving
0 = -2aln + 2alnx + -1a2ln

Solving for variable 'a'.
Remove the zero:
2aln + -2alnx + a2ln = -2aln + 2alnx + -1a2ln + 2aln + -2alnx + a2ln

Reorder the terms:
2aln + -2alnx + a2ln = -2aln + 2aln + 2alnx + -2alnx + -1a2ln + a2ln

Combine like terms: -2aln + 2aln = 0
2aln + -2alnx + a2ln = 0 + 2alnx + -2alnx + -1a2ln + a2ln
2aln + -2alnx + a2ln = 2alnx + -2alnx + -1a2ln + a2ln

Combine like terms: 2alnx + -2alnx = 0
2aln + -2alnx + a2ln = 0 + -1a2ln + a2ln
2aln + -2alnx + a2ln = -1a2ln + a2ln

Combine like terms: -1a2ln + a2ln = 0
2aln + -2alnx + a2ln = 0

Factor out the Greatest Common Factor (GCF), 'aln'.
aln(2 + -2x + a) = 0


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

Simplifying
aln = 0

Solving
aln = 0

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

Simplifying
aln = 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 '(2 + -2x + a)' equal to zero and attempt to solve:

Simplifying
2 + -2x + a = 0

Reorder the terms:
2 + a + -2x = 0

Solving
2 + a + -2x = 0

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

Add '-2' to each side of the equation.
2 + a + -2 + -2x = 0 + -2

Reorder the terms:
2 + -2 + a + -2x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a + -2x = 0 + -2
a + -2x = 0 + -2

Combine like terms: 0 + -2 = -2
a + -2x = -2

Add '2x' to each side of the equation.
a + -2x + 2x = -2 + 2x

Combine like terms: -2x + 2x = 0
a + 0 = -2 + 2x
a = -2 + 2x

Simplifying
a = -2 + 2x
Solution
a = {-2 + 2x}

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