2e^3x-2+4=16

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Solution for 2e^3x-2+4=16 equation: 


Simplifying
2e3x + -2 + 4 = 16

Reorder the terms:
-2 + 4 + 2e3x = 16

Combine like terms: -2 + 4 = 2
2 + 2e3x = 16

Solving
2 + 2e3x = 16

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 + 2e3x = 16 + -2

Combine like terms: 2 + -2 = 0
0 + 2e3x = 16 + -2
2e3x = 16 + -2

Combine like terms: 16 + -2 = 14
2e3x = 14

Divide each side by '2x'.
e3 = 7x-1

Simplifying
e3 = 7x-1

Combine like terms: 7x-1 + -7x-1 = 0
e3 + -7x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e3x + -7) = 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 + -7)' equal to zero and attempt to solve:

Simplifying
e3x + -7 = 0

Reorder the terms:
-7 + e3x = 0

Solving
-7 + e3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + e3x = 0 + 7

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

Combine like terms: 0 + 7 = 7
e3x = 7

Divide each side by 'x'.
e3 = 7x-1

Simplifying
e3 = 7x-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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