e(3x-5)*e(-x)=4e

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Solution for e(3x-5)*e(-x)=4e equation:


Simplifying
e(3x + -5) * e(-1x) = 4e

Reorder the terms:
e(-5 + 3x) * e(-1x) = 4e

Remove parenthesis around (-1x)
e(-5 + 3x) * e * -1x = 4e

Reorder the terms for easier multiplication:
-1e * e * x(-5 + 3x) = 4e

Multiply e * e
-1e2 * x(-5 + 3x) = 4e

Multiply e2 * x
-1e2x(-5 + 3x) = 4e
(-5 * -1e2x + 3x * -1e2x) = 4e
(5e2x + -3e2x2) = 4e

Solving
5e2x + -3e2x2 = 4e

Solving for variable 'e'.

Reorder the terms:
-4e + 5e2x + -3e2x2 = 4e + -4e

Combine like terms: 4e + -4e = 0
-4e + 5e2x + -3e2x2 = 0

Factor out the Greatest Common Factor (GCF), 'e'.
e(-4 + 5ex + -3ex2) = 0

Subproblem 1

Set the factor 'e' equal to zero and attempt to solve: Simplifying e = 0 Solving e = 0 Move all terms containing e to the left, all other terms to the right. Simplifying e = 0

Subproblem 2

Set the factor '(-4 + 5ex + -3ex2)' equal to zero and attempt to solve: Simplifying -4 + 5ex + -3ex2 = 0 Solving -4 + 5ex + -3ex2 = 0 Move all terms containing e to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 5ex + 4 + -3ex2 = 0 + 4 Reorder the terms: -4 + 4 + 5ex + -3ex2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5ex + -3ex2 = 0 + 4 5ex + -3ex2 = 0 + 4 Combine like terms: 0 + 4 = 4 5ex + -3ex2 = 4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

e = {0}

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