e^7x-2=-8

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Solution for e^7x-2=-8 equation:


Simplifying
e7x + -2 = -8

Reorder the terms:
-2 + e7x = -8

Solving
-2 + e7x = -8

Solving for variable 'e'.

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

Add '2' to each side of the equation.
-2 + 2 + e7x = -8 + 2

Combine like terms: -2 + 2 = 0
0 + e7x = -8 + 2
e7x = -8 + 2

Combine like terms: -8 + 2 = -6
e7x = -6

Divide each side by 'x'.
e7 = -6x-1

Simplifying
e7 = -6x-1

Combine like terms: -6x-1 + 6x-1 = 0
e7 + 6x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e7x + 6) = 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 '(e7x + 6)' equal to zero and attempt to solve: Simplifying e7x + 6 = 0 Reorder the terms: 6 + e7x = 0 Solving 6 + e7x = 0 Move all terms containing e to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + e7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + e7x = 0 + -6 e7x = 0 + -6 Combine like terms: 0 + -6 = -6 e7x = -6 Divide each side by 'x'. e7 = -6x-1 Simplifying e7 = -6x-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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