4e^2x-3=2

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

Simplifying
4e2x + -3 = 2

Reorder the terms:
-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 = 5
4e2x = 5

Divide each side by '4x'.
e2 = 1.25x-1

Simplifying
e2 = 1.25x-1

Combine like terms: 1.25x-1 + -1.25x-1 = 0.00
e2 + -1.25x-1 = 0.00

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -1.25) = 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 + -1.25)' equal to zero and attempt to solve:

Simplifying
e2x + -1.25 = 0

Reorder the terms:
-1.25 + e2x = 0

Solving
-1.25 + e2x = 0

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + e2x = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + e2x = 0 + 1.25
e2x = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
e2x = 1.25

Divide each side by 'x'.
e2 = 1.25x-1

Simplifying
e2 = 1.25x-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.