5e^2x+16=56

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Solution for 5e^2x+16=56 equation:


Simplifying
5e2x + 16 = 56

Reorder the terms:
16 + 5e2x = 56

Solving
16 + 5e2x = 56

Solving for variable 'e'.

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

Add '-16' to each side of the equation.
16 + -16 + 5e2x = 56 + -16

Combine like terms: 16 + -16 = 0
0 + 5e2x = 56 + -16
5e2x = 56 + -16

Combine like terms: 56 + -16 = 40
5e2x = 40

Divide each side by '5x'.
e2 = 8x-1

Simplifying
e2 = 8x-1

Combine like terms: 8x-1 + -8x-1 = 0
e2 + -8x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -8) = 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 '(e2x + -8)' equal to zero and attempt to solve: Simplifying e2x + -8 = 0 Reorder the terms: -8 + e2x = 0 Solving -8 + e2x = 0 Move all terms containing e to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + e2x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + e2x = 0 + 8 e2x = 0 + 8 Combine like terms: 0 + 8 = 8 e2x = 8 Divide each side by 'x'. e2 = 8x-1 Simplifying e2 = 8x-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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