xln(x+1)+2ln(x+1)-(x+1)ln(x+1)=

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


Simplifying
xln(x + 1) + 2ln(x + 1) + -1(x + 1) * ln(x + 1) = 0

Reorder the terms:
lnx(1 + x) + 2ln(x + 1) + -1(x + 1) * ln(x + 1) = 0
(1 * lnx + x * lnx) + 2ln(x + 1) + -1(x + 1) * ln(x + 1) = 0
(1lnx + lnx2) + 2ln(x + 1) + -1(x + 1) * ln(x + 1) = 0

Reorder the terms:
1lnx + lnx2 + 2ln(1 + x) + -1(x + 1) * ln(x + 1) = 0
1lnx + lnx2 + (1 * 2ln + x * 2ln) + -1(x + 1) * ln(x + 1) = 0
1lnx + lnx2 + (2ln + 2lnx) + -1(x + 1) * ln(x + 1) = 0

Reorder the terms:
1lnx + lnx2 + 2ln + 2lnx + -1(1 + x) * ln(x + 1) = 0

Reorder the terms:
1lnx + lnx2 + 2ln + 2lnx + -1(1 + x) * ln(1 + x) = 0

Reorder the terms for easier multiplication:
1lnx + lnx2 + 2ln + 2lnx + -1ln(1 + x)(1 + x) = 0

Multiply (1 + x) * (1 + x)
1lnx + lnx2 + 2ln + 2lnx + -1ln(1(1 + x) + x(1 + x)) = 0
1lnx + lnx2 + 2ln + 2lnx + -1ln((1 * 1 + x * 1) + x(1 + x)) = 0
1lnx + lnx2 + 2ln + 2lnx + -1ln((1 + 1x) + x(1 + x)) = 0
1lnx + lnx2 + 2ln + 2lnx + -1ln(1 + 1x + (1 * x + x * x)) = 0
1lnx + lnx2 + 2ln + 2lnx + -1ln(1 + 1x + (1x + x2)) = 0

Combine like terms: 1x + 1x = 2x
1lnx + lnx2 + 2ln + 2lnx + -1ln(1 + 2x + x2) = 0
1lnx + lnx2 + 2ln + 2lnx + (1 * -1ln + 2x * -1ln + x2 * -1ln) = 0
1lnx + lnx2 + 2ln + 2lnx + (-1ln + -2lnx + -1lnx2) = 0

Reorder the terms:
2ln + -1ln + 1lnx + 2lnx + -2lnx + lnx2 + -1lnx2 = 0

Combine like terms: 2ln + -1ln = 1ln
1ln + 1lnx + 2lnx + -2lnx + lnx2 + -1lnx2 = 0

Combine like terms: 1lnx + 2lnx = 3lnx
1ln + 3lnx + -2lnx + lnx2 + -1lnx2 = 0

Combine like terms: 3lnx + -2lnx = 1lnx
1ln + 1lnx + lnx2 + -1lnx2 = 0

Combine like terms: lnx2 + -1lnx2 = 0
1ln + 1lnx + 0 = 0
1ln + 1lnx = 0

Solving
1ln + 1lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + x) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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