3e^3x-1=12

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Solution for 3e^3x-1=12 equation:


Simplifying
3e3x + -1 = 12

Reorder the terms:
-1 + 3e3x = 12

Solving
-1 + 3e3x = 12

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 + 3e3x = 12 + 1

Combine like terms: -1 + 1 = 0
0 + 3e3x = 12 + 1
3e3x = 12 + 1

Combine like terms: 12 + 1 = 13
3e3x = 13

Divide each side by '3x'.
e3 = 4.333333333x-1

Simplifying
e3 = 4.333333333x-1

Combine like terms: 4.333333333x-1 + -4.333333333x-1 = 0.000000000
e3 + -4.333333333x-1 = 0.000000000

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e3x + -4.333333333) = 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 '(e3x + -4.333333333)' equal to zero and attempt to solve: Simplifying e3x + -4.333333333 = 0 Reorder the terms: -4.333333333 + e3x = 0 Solving -4.333333333 + e3x = 0 Move all terms containing e to the left, all other terms to the right. Add '4.333333333' to each side of the equation. -4.333333333 + 4.333333333 + e3x = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + e3x = 0 + 4.333333333 e3x = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 e3x = 4.333333333 Divide each side by 'x'. e3 = 4.333333333x-1 Simplifying e3 = 4.333333333x-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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