2(1+e^2x)=5

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Solution for 2(1+e^2x)=5 equation: 


Simplifying
2(1 + e2x) = 5
(1 * 2 + e2x * 2) = 5
(2 + 2e2x) = 5

Solving
2 + 2e2x = 5

Solving for variable 'e'.

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

Add '-2' to each side of the equation.
2 + -2 + 2e2x = 5 + -2

Combine like terms: 2 + -2 = 0
0 + 2e2x = 5 + -2
2e2x = 5 + -2

Combine like terms: 5 + -2 = 3
2e2x = 3

Divide each side by '2x'.
e2 = 1.5x-1

Simplifying
e2 = 1.5x-1

Combine like terms: 1.5x-1 + -1.5x-1 = 0.0
e2 + -1.5x-1 = 0.0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -1.5) = 0.0


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 + -1.5)' equal to zero and attempt to solve:

Simplifying
e2x + -1.5 = 0

Reorder the terms:
-1.5 + e2x = 0

Solving
-1.5 + e2x = 0

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + e2x = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + e2x = 0 + 1.5
e2x = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
e2x = 1.5

Divide each side by 'x'.
e2 = 1.5x-1

Simplifying
e2 = 1.5x-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.

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