7=(3(e^4x)+1)

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Solution for 7=(3(e^4x)+1) equation:


Simplifying
7 = (3(e4x) + 1)

Reorder the terms:
7 = (1 + 3e4x)

Remove parenthesis around (1 + 3e4x)
7 = 1 + 3e4x

Solving
7 = 1 + 3e4x

Solving for variable 'e'.

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

Add '-3e4x' to each side of the equation.
7 + -3e4x = 1 + 3e4x + -3e4x

Combine like terms: 3e4x + -3e4x = 0
7 + -3e4x = 1 + 0
7 + -3e4x = 1

Add '-7' to each side of the equation.
7 + -7 + -3e4x = 1 + -7

Combine like terms: 7 + -7 = 0
0 + -3e4x = 1 + -7
-3e4x = 1 + -7

Combine like terms: 1 + -7 = -6
-3e4x = -6

Divide each side by '-3x'.
e4 = 2x-1

Simplifying
e4 = 2x-1

Combine like terms: 2x-1 + -2x-1 = 0
e4 + -2x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e4x + -2) = 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 + -2)' equal to zero and attempt to solve: Simplifying e4x + -2 = 0 Reorder the terms: -2 + e4x = 0 Solving -2 + e4x = 0 Move all terms containing e to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + e4x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + e4x = 0 + 2 e4x = 0 + 2 Combine like terms: 0 + 2 = 2 e4x = 2 Divide each side by 'x'. e4 = 2x-1 Simplifying e4 = 2x-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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