85=16e^2x+1

Solution for 85=16e^2x+1 equation:

Simplifying
85 = 16e2x + 1

Reorder the terms:
85 = 1 + 16e2x

Solving
85 = 1 + 16e2x

Solving for variable 'e'.

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

Add '-16e2x' to each side of the equation.
85 + -16e2x = 1 + 16e2x + -16e2x

Combine like terms: 16e2x + -16e2x = 0
85 + -16e2x = 1 + 0
85 + -16e2x = 1

Add '-85' to each side of the equation.
85 + -85 + -16e2x = 1 + -85

Combine like terms: 85 + -85 = 0
0 + -16e2x = 1 + -85
-16e2x = 1 + -85

Combine like terms: 1 + -85 = -84
-16e2x = -84

Divide each side by '-16x'.
e2 = 5.25x-1

Simplifying
e2 = 5.25x-1

Combine like terms: 5.25x-1 + -5.25x-1 = 0.00
e2 + -5.25x-1 = 0.00

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -5.25) = 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 '(e2x + -5.25)' equal to zero and attempt to solve:

Simplifying
e2x + -5.25 = 0

Reorder the terms:
-5.25 + e2x = 0

Solving
-5.25 + e2x = 0

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + e2x = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + e2x = 0 + 5.25
e2x = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
e2x = 5.25

Divide each side by 'x'.
e2 = 5.25x-1

Simplifying
e2 = 5.25x-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.