(2x^2-8)*(e^2x-6)=0

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Solution for (2x^2-8)*(e^2x-6)=0 equation: 


Simplifying
(2x2 + -8)(e2x + -6) = 0

Reorder the terms:
(-8 + 2x2)(e2x + -6) = 0

Reorder the terms:
(-8 + 2x2)(-6 + e2x) = 0

Multiply (-8 + 2x2) * (-6 + e2x)
(-8(-6 + e2x) + 2x2 * (-6 + e2x)) = 0
((-6 * -8 + e2x * -8) + 2x2 * (-6 + e2x)) = 0
((48 + -8e2x) + 2x2 * (-6 + e2x)) = 0
(48 + -8e2x + (-6 * 2x2 + e2x * 2x2)) = 0

Reorder the terms:
(48 + -8e2x + (2e2x3 + -12x2)) = 0
(48 + -8e2x + (2e2x3 + -12x2)) = 0
(48 + -8e2x + 2e2x3 + -12x2) = 0

Solving
48 + -8e2x + 2e2x3 + -12x2 = 0

Solving for variable 'e'.

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

Add '-48' to each side of the equation.
48 + -8e2x + 2e2x3 + -48 + -12x2 = 0 + -48

Reorder the terms:
48 + -48 + -8e2x + 2e2x3 + -12x2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -8e2x + 2e2x3 + -12x2 = 0 + -48
-8e2x + 2e2x3 + -12x2 = 0 + -48

Combine like terms: 0 + -48 = -48
-8e2x + 2e2x3 + -12x2 = -48

Add '12x2' to each side of the equation.
-8e2x + 2e2x3 + -12x2 + 12x2 = -48 + 12x2

Combine like terms: -12x2 + 12x2 = 0
-8e2x + 2e2x3 + 0 = -48 + 12x2
-8e2x + 2e2x3 = -48 + 12x2

Reorder the terms:
48 + -8e2x + 2e2x3 + -12x2 = -48 + 12x2 + 48 + -12x2

Reorder the terms:
48 + -8e2x + 2e2x3 + -12x2 = -48 + 48 + 12x2 + -12x2

Combine like terms: -48 + 48 = 0
48 + -8e2x + 2e2x3 + -12x2 = 0 + 12x2 + -12x2
48 + -8e2x + 2e2x3 + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
48 + -8e2x + 2e2x3 + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -4e2x + e2x3 + -6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(24 + -4e2x + e2x3 + -6x2)' equal to zero and attempt to solve:

Simplifying
24 + -4e2x + e2x3 + -6x2 = 0

Solving
24 + -4e2x + e2x3 + -6x2 = 0

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

Add '-24' to each side of the equation.
24 + -4e2x + e2x3 + -24 + -6x2 = 0 + -24

Reorder the terms:
24 + -24 + -4e2x + e2x3 + -6x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -4e2x + e2x3 + -6x2 = 0 + -24
-4e2x + e2x3 + -6x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-4e2x + e2x3 + -6x2 = -24

Add '6x2' to each side of the equation.
-4e2x + e2x3 + -6x2 + 6x2 = -24 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-4e2x + e2x3 + 0 = -24 + 6x2
-4e2x + e2x3 = -24 + 6x2

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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