3-4e^2x=2

Solution for 3-4e^2x=2 equation:

Simplifying
3 + -4e2x = 2

Solving
3 + -4e2x = 2

Solving for variable 'e'.

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

Add '-3' to each side of the equation.
3 + -3 + -4e2x = 2 + -3

Combine like terms: 3 + -3 = 0
0 + -4e2x = 2 + -3
-4e2x = 2 + -3

Combine like terms: 2 + -3 = -1
-4e2x = -1

Divide each side by '-4x'.
e2 = 0.25x-1

Simplifying
e2 = 0.25x-1

Combine like terms: 0.25x-1 + -0.25x-1 = 0.00
e2 + -0.25x-1 = 0.00

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -0.25) = 0.00

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

Simplifying
x-1 = 0

Solving
x-1 = 0

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

Add '-1x-1' to each side of the equation.
x-1 + -1x-1 = 0 + -1x-1
Remove the zero:
0 = -1x-1

Simplifying
0 = -1x-1

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 '(e2x + -0.25)' equal to zero and attempt to solve:

Simplifying
e2x + -0.25 = 0

Reorder the terms:
-0.25 + e2x = 0

Solving
-0.25 + e2x = 0

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + e2x = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + e2x = 0 + 0.25
e2x = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
e2x = 0.25

Divide each side by 'x'.
e2 = 0.25x-1

Simplifying
e2 = 0.25x-1

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.