3e^2x+1=9

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Solution for 3e^2x+1=9 equation:


Simplifying
3e2x + 1 = 9

Reorder the terms:
1 + 3e2x = 9

Solving
1 + 3e2x = 9

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 = 9 + -1

Combine like terms: 1 + -1 = 0
0 + 3e2x = 9 + -1
3e2x = 9 + -1

Combine like terms: 9 + -1 = 8
3e2x = 8

Divide each side by '3x'.
e2 = 2.666666667x-1

Simplifying
e2 = 2.666666667x-1

Combine like terms: 2.666666667x-1 + -2.666666667x-1 = 0.000000000
e2 + -2.666666667x-1 = 0.000000000

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -2.666666667) = 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 + -2.666666667)' equal to zero and attempt to solve: Simplifying e2x + -2.666666667 = 0 Reorder the terms: -2.666666667 + e2x = 0 Solving -2.666666667 + e2x = 0 Move all terms containing e to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + e2x = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + e2x = 0 + 2.666666667 e2x = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 e2x = 2.666666667 Divide each side by 'x'. e2 = 2.666666667x-1 Simplifying e2 = 2.666666667x-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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