7e^3x-6=27

Solution for 7e^3x-6=27 equation:

Simplifying
7e3x + -6 = 27

Reorder the terms:
-6 + 7e3x = 27

Solving
-6 + 7e3x = 27

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 + 7e3x = 27 + 6

Combine like terms: -6 + 6 = 0
0 + 7e3x = 27 + 6
7e3x = 27 + 6

Combine like terms: 27 + 6 = 33
7e3x = 33

Divide each side by '7x'.
e3 = 4.714285714x-1

Simplifying
e3 = 4.714285714x-1

Combine like terms: 4.714285714x-1 + -4.714285714x-1 = 0.000000000
e3 + -4.714285714x-1 = 0.000000000

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e3x + -4.714285714) = 0.000000000

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 + -4.714285714)' equal to zero and attempt to solve:

Simplifying
e3x + -4.714285714 = 0

Reorder the terms:
-4.714285714 + e3x = 0

Solving
-4.714285714 + e3x = 0

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

Add '4.714285714' to each side of the equation.
-4.714285714 + 4.714285714 + e3x = 0 + 4.714285714

Combine like terms: -4.714285714 + 4.714285714 = 0.000000000
0.000000000 + e3x = 0 + 4.714285714
e3x = 0 + 4.714285714

Combine like terms: 0 + 4.714285714 = 4.714285714
e3x = 4.714285714

Divide each side by 'x'.
e3 = 4.714285714x-1

Simplifying
e3 = 4.714285714x-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.