G(x)=x[lnx^4+lnx-2lnx]

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Solution for G(x)=x[lnx^4+lnx-2lnx] equation: 


Simplifying
G(x) = x[lnx4 + lnx + -2lnx]

Multiply G * x
xG = x[lnx4 + lnx + -2lnx]

Reorder the terms:
xG = x[lnx + -2lnx + lnx4]

Combine like terms: lnx + -2lnx = -1lnx
xG = x[-1lnx + lnx4]
xG = [-1lnx * x + lnx4 * x]
xG = [-1lnx2 + lnx5]

Solving
xG = -1lnx2 + lnx5

Solving for variable 'x'.

Reorder the terms:
lnx2 + -1lnx5 + xG = -1lnx2 + lnx5 + lnx2 + -1lnx5

Reorder the terms:
lnx2 + -1lnx5 + xG = -1lnx2 + lnx2 + lnx5 + -1lnx5

Combine like terms: -1lnx2 + lnx2 = 0
lnx2 + -1lnx5 + xG = 0 + lnx5 + -1lnx5
lnx2 + -1lnx5 + xG = lnx5 + -1lnx5

Combine like terms: lnx5 + -1lnx5 = 0
lnx2 + -1lnx5 + xG = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(lnx + -1lnx4 + 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 '(lnx + -1lnx4 + G)' equal to zero and attempt to solve:

Simplifying
lnx + -1lnx4 + G = 0

Reorder the terms:
G + lnx + -1lnx4 = 0

Solving
G + lnx + -1lnx4 = 0

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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