x=exp(-1)

Solution for x=exp(-1) equation:

Simplifying
x = exp(-1)

Reorder the terms for easier multiplication:
x = -1epx

Solving
x = -1epx

Solving for variable 'x'.

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

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

Combine like terms: -1epx + epx = 0
epx + x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(ep + 1) = 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 '(ep + 1)' equal to zero and attempt to solve:

Simplifying
ep + 1 = 0

Reorder the terms:
1 + ep = 0

Solving
1 + ep = 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 + ep = 0 + -1

Combine like terms: 1 + -1 = 0
0 + ep = 0 + -1
ep = 0 + -1

Combine like terms: 0 + -1 = -1
ep = -1

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

Combine like terms: ep + -1ep = 0
0 = -1 + -1ep

Simplifying
0 = -1 + -1ep

The solution to this equation could not be determined.

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