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

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


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

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

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

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

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

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

Solving
4e2x + -3e2x2 = 3e

Solving for variable 'e'.

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

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

Factor out the Greatest Common Factor (GCF), 'e'.
e(-3 + 4ex + -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 '(-3 + 4ex + -3ex2)' equal to zero and attempt to solve:

Simplifying
-3 + 4ex + -3ex2 = 0

Solving
-3 + 4ex + -3ex2 = 0

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

Add '3' to each side of the equation.
-3 + 4ex + 3 + -3ex2 = 0 + 3

Reorder the terms:
-3 + 3 + 4ex + -3ex2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4ex + -3ex2 = 0 + 3
4ex + -3ex2 = 0 + 3

Combine like terms: 0 + 3 = 3
4ex + -3ex2 = 3

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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