2e^3x-1=7

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Solution for 2e^3x-1=7 equation: 


Simplifying
2e3x + -1 = 7

Reorder the terms:
-1 + 2e3x = 7

Solving
-1 + 2e3x = 7

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 + 2e3x = 7 + 1

Combine like terms: -1 + 1 = 0
0 + 2e3x = 7 + 1
2e3x = 7 + 1

Combine like terms: 7 + 1 = 8
2e3x = 8

Divide each side by '2x'.
e3 = 4x-1

Simplifying
e3 = 4x-1

Combine like terms: 4x-1 + -4x-1 = 0
e3 + -4x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e3x + -4) = 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 '(e3x + -4)' equal to zero and attempt to solve:

Simplifying
e3x + -4 = 0

Reorder the terms:
-4 + e3x = 0

Solving
-4 + e3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + e3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + e3x = 0 + 4
e3x = 0 + 4

Combine like terms: 0 + 4 = 4
e3x = 4

Divide each side by 'x'.
e3 = 4x-1

Simplifying
e3 = 4x-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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