(e^6x)+(e^4x)-(2e^2x)=0

Solution for (e^6x)+(e^4x)-(2e^2x)=0 equation:

Simplifying
(e6x) + (e4x) + -1(2e2x) = 0
e6x + (e4x) + -1(2e2x) = 0
e6x + e4x + -1(2e2x) = 0

Remove parenthesis around (2e2x)
e6x + e4x + -1 * 2e2x = 0

Multiply -1 * 2
e6x + e4x + -2e2x = 0

Reorder the terms:
-2e2x + e4x + e6x = 0

Solving
-2e2x + e4x + e6x = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), 'e2x'.
e2x(-2 + e2 + e4) = 0

Factor a trinomial.
e2x((-2 + -1e2)(1 + -1e2)) = 0

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

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 '(-2 + -1e2)' equal to zero and attempt to solve:

Simplifying
-2 + -1e2 = 0

Solving
-2 + -1e2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1e2 = 0 + 2

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

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

Divide each side by '-1'.
e2 = -2

Simplifying
e2 = -2

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 + e)' equal to zero and attempt to solve:

Simplifying
1 + e = 0

Solving
1 + e = 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 + e = 0 + -1

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

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

Simplifying
e = -1
Subproblem 4
Set the factor '(1 + -1e)' equal to zero and attempt to solve:

Simplifying
1 + -1e = 0

Solving
1 + -1e = 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 + -1e = 0 + -1

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

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

Divide each side by '-1'.
e = 1

Simplifying
e = 1
Solution
e = {-1, 1}