3e^4x+6=18

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Solution for 3e^4x+6=18 equation:


Simplifying
3e4x + 6 = 18

Reorder the terms:
6 + 3e4x = 18

Solving
6 + 3e4x = 18

Solving for variable 'e'.

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

Add '-6' to each side of the equation.
6 + -6 + 3e4x = 18 + -6

Combine like terms: 6 + -6 = 0
0 + 3e4x = 18 + -6
3e4x = 18 + -6

Combine like terms: 18 + -6 = 12
3e4x = 12

Divide each side by '3x'.
e4 = 4x-1

Simplifying
e4 = 4x-1

Combine like terms: 4x-1 + -4x-1 = 0
e4 + -4x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e4x + -4) = 0

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 '(e4x + -4)' equal to zero and attempt to solve: Simplifying e4x + -4 = 0 Reorder the terms: -4 + e4x = 0 Solving -4 + e4x = 0 Move all terms containing e to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + e4x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + e4x = 0 + 4 e4x = 0 + 4 Combine like terms: 0 + 4 = 4 e4x = 4 Divide each side by 'x'. e4 = 4x-1 Simplifying e4 = 4x-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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