5e^3x+1-7=13

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Solution for 5e^3x+1-7=13 equation: 


Simplifying
5e3x + 1 + -7 = 13

Reorder the terms:
1 + -7 + 5e3x = 13

Combine like terms: 1 + -7 = -6
-6 + 5e3x = 13

Solving
-6 + 5e3x = 13

Solving for variable 'e'.

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

Add '6' to each side of the equation.
-6 + 6 + 5e3x = 13 + 6

Combine like terms: -6 + 6 = 0
0 + 5e3x = 13 + 6
5e3x = 13 + 6

Combine like terms: 13 + 6 = 19
5e3x = 19

Divide each side by '5x'.
e3 = 3.8x-1

Simplifying
e3 = 3.8x-1

Combine like terms: 3.8x-1 + -3.8x-1 = 0.0
e3 + -3.8x-1 = 0.0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e3x + -3.8) = 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 '(e3x + -3.8)' equal to zero and attempt to solve:

Simplifying
e3x + -3.8 = 0

Reorder the terms:
-3.8 + e3x = 0

Solving
-3.8 + e3x = 0

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

Add '3.8' to each side of the equation.
-3.8 + 3.8 + e3x = 0 + 3.8

Combine like terms: -3.8 + 3.8 = 0.0
0.0 + e3x = 0 + 3.8
e3x = 0 + 3.8

Combine like terms: 0 + 3.8 = 3.8
e3x = 3.8

Divide each side by 'x'.
e3 = 3.8x-1

Simplifying
e3 = 3.8x-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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