300=200e^2t

Solution for 300=200e^2t equation:

Simplifying
300 = 200e2t

Solving
300 = 200e2t

Solving for variable 'e'.

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

Add '-200e2t' to each side of the equation.
300 + -200e2t = 200e2t + -200e2t

Combine like terms: 200e2t + -200e2t = 0
300 + -200e2t = 0

Add '-300' to each side of the equation.
300 + -300 + -200e2t = 0 + -300

Combine like terms: 300 + -300 = 0
0 + -200e2t = 0 + -300
-200e2t = 0 + -300

Combine like terms: 0 + -300 = -300
-200e2t = -300

Divide each side by '-200t'.
e2 = 1.5t-1

Simplifying
e2 = 1.5t-1

Combine like terms: 1.5t-1 + -1.5t-1 = 0.0
e2 + -1.5t-1 = 0.0

Factor out the Greatest Common Factor (GCF), 't-1'.
t-1(e2t + -1.5) = 0.0

Subproblem 1
Set the factor 't-1' equal to zero and attempt to solve:

Simplifying
t-1 = 0

Solving
t-1 = 0

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

Add '-1t-1' to each side of the equation.
t-1 + -1t-1 = 0 + -1t-1
Remove the zero:
0 = -1t-1

Simplifying
0 = -1t-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 '(e2t + -1.5)' equal to zero and attempt to solve:

Simplifying
e2t + -1.5 = 0

Reorder the terms:
-1.5 + e2t = 0

Solving
-1.5 + e2t = 0

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + e2t = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + e2t = 0 + 1.5
e2t = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
e2t = 1.5

Divide each side by 't'.
e2 = 1.5t-1

Simplifying
e2 = 1.5t-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.