2e^2x-1=12

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Solution for 2e^2x-1=12 equation: 


Simplifying
2e2x + -1 = 12

Reorder the terms:
-1 + 2e2x = 12

Solving
-1 + 2e2x = 12

Solving for variable 'e'.

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

Add '1' to each side of the equation.
-1 + 1 + 2e2x = 12 + 1

Combine like terms: -1 + 1 = 0
0 + 2e2x = 12 + 1
2e2x = 12 + 1

Combine like terms: 12 + 1 = 13
2e2x = 13

Divide each side by '2x'.
e2 = 6.5x-1

Simplifying
e2 = 6.5x-1

Combine like terms: 6.5x-1 + -6.5x-1 = 0.0
e2 + -6.5x-1 = 0.0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -6.5) = 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 + -6.5)' equal to zero and attempt to solve:

Simplifying
e2x + -6.5 = 0

Reorder the terms:
-6.5 + e2x = 0

Solving
-6.5 + e2x = 0

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + e2x = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + e2x = 0 + 6.5
e2x = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
e2x = 6.5

Divide each side by 'x'.
e2 = 6.5x-1

Simplifying
e2 = 6.5x-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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