3(e^2x)-7=50

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Solution for 3(e^2x)-7=50 equation: 


Simplifying
3(e2x) + -7 = 50

Reorder the terms:
-7 + 3e2x = 50

Solving
-7 + 3e2x = 50

Solving for variable 'e'.

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

Add '7' to each side of the equation.
-7 + 7 + 3e2x = 50 + 7

Combine like terms: -7 + 7 = 0
0 + 3e2x = 50 + 7
3e2x = 50 + 7

Combine like terms: 50 + 7 = 57
3e2x = 57

Divide each side by '3x'.
e2 = 19x-1

Simplifying
e2 = 19x-1

Combine like terms: 19x-1 + -19x-1 = 0
e2 + -19x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -19) = 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 '(e2x + -19)' equal to zero and attempt to solve:

Simplifying
e2x + -19 = 0

Reorder the terms:
-19 + e2x = 0

Solving
-19 + e2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + e2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + e2x = 0 + 19
e2x = 0 + 19

Combine like terms: 0 + 19 = 19
e2x = 19

Divide each side by 'x'.
e2 = 19x-1

Simplifying
e2 = 19x-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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