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

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


Simplifying
0 = ((4e2x) + -1(6e6x))

Remove parenthesis around (6e6x)
0 = ((4e2x) + -1 * 6e6x)

Multiply -1 * 6
0 = ((4e2x) + -6e6x)

Remove parenthesis around ((4e2x) + -6e6x)
0 = (4e2x) + -6e6x

Solving
0 = (4e2x) + -6e6x

Solving for variable 'e'.
Remove the zero:
(-4e2x) + 6e6x = (4e2x) + -6e6x + (-4e2x) + 6e6x

Reorder the terms:
(-4e2x) + 6e6x = (4e2x) + (-4e2x) + -6e6x + 6e6x

Combine like terms: (4e2x) + (-4e2x) = 0
(-4e2x) + 6e6x = 0 + -6e6x + 6e6x
(-4e2x) + 6e6x = -6e6x + 6e6x

Combine like terms: -6e6x + 6e6x = 0
(-4e2x) + 6e6x = 0

Factor out the Greatest Common Factor (GCF), '2e2x'.
2e2x(-2 + 3e4) = 0

Ignore the factor 2.

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 + 3e4)' equal to zero and attempt to solve:

Simplifying
-2 + 3e4 = 0

Solving
-2 + 3e4 = 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 + 3e4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3e4 = 0 + 2
3e4 = 0 + 2

Combine like terms: 0 + 2 = 2
3e4 = 2

Divide each side by '3'.
e4 = 0.6666666667

Simplifying
e4 = 0.6666666667

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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