G(x)=x+lnx

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Solution for G(x)=x+lnx equation: 


Simplifying
G(x) = x + lnx

Multiply G * x
xG = x + lnx

Reorder the terms:
xG = lnx + x

Solving
xG = lnx + x

Solving for variable 'x'.

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

Add '-1lnx' to each side of the equation.
-1lnx + xG = lnx + -1lnx + x

Combine like terms: lnx + -1lnx = 0
-1lnx + xG = 0 + x
-1lnx + xG = x

Add '-1x' to each side of the equation.
-1lnx + -1x + xG = x + -1x

Combine like terms: x + -1x = 0
-1lnx + -1x + xG = 0

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


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 + -1 + G)' equal to zero and attempt to solve:

Simplifying
-1ln + -1 + G = 0

Reorder the terms:
-1 + G + -1ln = 0

Solving
-1 + G + -1ln = 0

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

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

Reorder the terms:
-1 + 1 + G + -1ln = 0 + 1

Combine like terms: -1 + 1 = 0
0 + G + -1ln = 0 + 1
G + -1ln = 0 + 1

Combine like terms: 0 + 1 = 1
G + -1ln = 1

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

Combine like terms: G + -1G = 0
0 + -1ln = 1 + -1G
-1ln = 1 + -1G

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

Combine like terms: -1ln + ln = 0
0 = 1 + -1G + ln

Simplifying
0 = 1 + -1G + ln

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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