2e^3x=8e^5x

Solution for 2e^3x=8e^5x equation:

Simplifying
2e3x = 8e5x

Solving
2e3x = 8e5x

Solving for variable 'e'.

Combine like terms: 8e5x + -8e5x = 0
2e3x + -8e5x = 0

Factor out the Greatest Common Factor (GCF), '2e3x'.
2e3x(1 + -4e2) = 0

Factor a difference between two squares.
2e3x((1 + 2e)(1 + -2e)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'e3x' equal to zero and attempt to solve:

Simplifying
e3x = 0

Solving
e3x = 0

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

Simplifying
e3x = 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 + 2e)' equal to zero and attempt to solve:

Simplifying
1 + 2e = 0

Solving
1 + 2e = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2e = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2e = 0 + -1
2e = 0 + -1

Combine like terms: 0 + -1 = -1
2e = -1

Divide each side by '2'.
e = -0.5

Simplifying
e = -0.5
Subproblem 3
Set the factor '(1 + -2e)' equal to zero and attempt to solve:

Simplifying
1 + -2e = 0

Solving
1 + -2e = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2e = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2e = 0 + -1
-2e = 0 + -1

Combine like terms: 0 + -1 = -1
-2e = -1

Divide each side by '-2'.
e = 0.5

Simplifying
e = 0.5
Solution
e = {-0.5, 0.5}