4(e^2x-3)-12=20

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Solution for 4(e^2x-3)-12=20 equation: 


Simplifying
4(e2x + -3) + -12 = 20

Reorder the terms:
4(-3 + e2x) + -12 = 20
(-3 * 4 + e2x * 4) + -12 = 20
(-12 + 4e2x) + -12 = 20

Reorder the terms:
-12 + -12 + 4e2x = 20

Combine like terms: -12 + -12 = -24
-24 + 4e2x = 20

Solving
-24 + 4e2x = 20

Solving for variable 'e'.

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

Add '24' to each side of the equation.
-24 + 24 + 4e2x = 20 + 24

Combine like terms: -24 + 24 = 0
0 + 4e2x = 20 + 24
4e2x = 20 + 24

Combine like terms: 20 + 24 = 44
4e2x = 44

Divide each side by '4x'.
e2 = 11x-1

Simplifying
e2 = 11x-1

Combine like terms: 11x-1 + -11x-1 = 0
e2 + -11x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -11) = 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 + -11)' equal to zero and attempt to solve:

Simplifying
e2x + -11 = 0

Reorder the terms:
-11 + e2x = 0

Solving
-11 + e2x = 0

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

Add '11' to each side of the equation.
-11 + 11 + e2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + e2x = 0 + 11
e2x = 0 + 11

Combine like terms: 0 + 11 = 11
e2x = 11

Divide each side by 'x'.
e2 = 11x-1

Simplifying
e2 = 11x-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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