e^3x=5e^3x-7

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


Simplifying
e3x = 5e3x + -7

Reorder the terms:
e3x = -7 + 5e3x

Solving
e3x = -7 + 5e3x

Solving for variable 'e'.

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

Add '-5e3x' to each side of the equation.
e3x + -5e3x = -7 + 5e3x + -5e3x

Combine like terms: e3x + -5e3x = -4e3x
-4e3x = -7 + 5e3x + -5e3x

Combine like terms: 5e3x + -5e3x = 0
-4e3x = -7 + 0
-4e3x = -7

Divide each side by '-4x'.
e3 = 1.75x-1

Simplifying
e3 = 1.75x-1

Combine like terms: 1.75x-1 + -1.75x-1 = 0.00
e3 + -1.75x-1 = 0.00

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e3x + -1.75) = 0.00


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 + -1.75)' equal to zero and attempt to solve:

Simplifying
e3x + -1.75 = 0

Reorder the terms:
-1.75 + e3x = 0

Solving
-1.75 + e3x = 0

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + e3x = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + e3x = 0 + 1.75
e3x = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
e3x = 1.75

Divide each side by 'x'.
e3 = 1.75x-1

Simplifying
e3 = 1.75x-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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