3e^2x+1=5

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Solution for 3e^2x+1=5 equation:


Simplifying
3e2x + 1 = 5

Reorder the terms:
1 + 3e2x = 5

Solving
1 + 3e2x = 5

Solving for variable 'e'.

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

Add '-1' to each side of the equation.
1 + -1 + 3e2x = 5 + -1

Combine like terms: 1 + -1 = 0
0 + 3e2x = 5 + -1
3e2x = 5 + -1

Combine like terms: 5 + -1 = 4
3e2x = 4

Divide each side by '3x'.
e2 = 1.333333333x-1

Simplifying
e2 = 1.333333333x-1

Combine like terms: 1.333333333x-1 + -1.333333333x-1 = 0.000000000
e2 + -1.333333333x-1 = 0.000000000

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -1.333333333) = 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 '(e2x + -1.333333333)' equal to zero and attempt to solve: Simplifying e2x + -1.333333333 = 0 Reorder the terms: -1.333333333 + e2x = 0 Solving -1.333333333 + e2x = 0 Move all terms containing e to the left, all other terms to the right. Add '1.333333333' to each side of the equation. -1.333333333 + 1.333333333 + e2x = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + e2x = 0 + 1.333333333 e2x = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 e2x = 1.333333333 Divide each side by 'x'. e2 = 1.333333333x-1 Simplifying e2 = 1.333333333x-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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