9e^2x=36e^6x

Solution for 9e^2x=36e^6x equation:

Simplifying
9e2x = 36e6x

Solving
9e2x = 36e6x

Solving for variable 'e'.

Combine like terms: 36e6x + -36e6x = 0
9e2x + -36e6x = 0

Factor out the Greatest Common Factor (GCF), '9e2x'.
9e2x(1 + -4e4) = 0

Factor a difference between two squares.
9e2x((1 + 2e2)(1 + -2e2)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor 'e2x' equal to zero and attempt to solve:

Simplifying
e2x = 0

Solving
e2x = 0

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

Simplifying
e2x = 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 + 2e2)' equal to zero and attempt to solve:

Simplifying
1 + 2e2 = 0

Solving
1 + 2e2 = 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 + 2e2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2e2 = 0 + -1
2e2 = 0 + -1

Combine like terms: 0 + -1 = -1
2e2 = -1

Divide each side by '2'.
e2 = -0.5

Simplifying
e2 = -0.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + -2e2)' equal to zero and attempt to solve:

Simplifying
1 + -2e2 = 0

Solving
1 + -2e2 = 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 + -2e2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2e2 = 0 + -1
-2e2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2e2 = -1

Divide each side by '-2'.
e2 = 0.5

Simplifying
e2 = 0.5

Take the square root of each side:
e = {-0.707106781, 0.707106781}
Solution
e = {-0.707106781, 0.707106781}