-x=ln(8e^2x)

Solution for -x=ln(8e^2x) equation:

Simplifying
-1x = ln(8e2x)

Remove parenthesis around (8e2x)
-1x = ln * 8e2x

Reorder the terms for easier multiplication:
-1x = 8ln * e2x

Multiply ln * e2x
-1x = 8e2lnx

Solving
-1x = 8e2lnx

Solving for variable 'x'.

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

Add '-8e2lnx' to each side of the equation.
-8e2lnx + -1x = 8e2lnx + -8e2lnx

Combine like terms: 8e2lnx + -8e2lnx = 0
-8e2lnx + -1x = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(8e2ln + 1) = 0

Ignore the factor -1.
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 '(8e2ln + 1)' equal to zero and attempt to solve:

Simplifying
8e2ln + 1 = 0

Reorder the terms:
1 + 8e2ln = 0

Solving
1 + 8e2ln = 0

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

Add '-1' to each side of the equation.
1 + -1 + 8e2ln = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8e2ln = 0 + -1
8e2ln = 0 + -1

Combine like terms: 0 + -1 = -1
8e2ln = -1

Add '-8e2ln' to each side of the equation.
8e2ln + -8e2ln = -1 + -8e2ln

Combine like terms: 8e2ln + -8e2ln = 0
0 = -1 + -8e2ln

Simplifying
0 = -1 + -8e2ln

The solution to this equation could not be determined.

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