e^6x=9e^4x

Solution for e^6x=9e^4x equation:

Simplifying
e6x = 9e4x

Solving
e6x = 9e4x

Solving for variable 'e'.

Reorder the terms:
-9e4x + e6x = 9e4x + -9e4x

Combine like terms: 9e4x + -9e4x = 0
-9e4x + e6x = 0

Factor out the Greatest Common Factor (GCF), 'e4x'.
e4x(-9 + e2) = 0

Factor a difference between two squares.
e4x((3 + e)(-3 + e)) = 0

Subproblem 1
Set the factor 'e4x' equal to zero and attempt to solve:

Simplifying
e4x = 0

Solving
e4x = 0

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

Simplifying
e4x = 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 '(3 + e)' equal to zero and attempt to solve:

Simplifying
3 + e = 0

Solving
3 + e = 0

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

Add '-3' to each side of the equation.
3 + -3 + e = 0 + -3

Combine like terms: 3 + -3 = 0
0 + e = 0 + -3
e = 0 + -3

Combine like terms: 0 + -3 = -3
e = -3

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

Simplifying
-3 + e = 0

Solving
-3 + e = 0

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

Add '3' to each side of the equation.
-3 + 3 + e = 0 + 3

Combine like terms: -3 + 3 = 0
0 + e = 0 + 3
e = 0 + 3

Combine like terms: 0 + 3 = 3
e = 3

Simplifying
e = 3
Solution
e = {-3, 3}