(e(2x)-3e(3x))-(4e(2x)-5)=0

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Solution for (e(2x)-3e(3x))-(4e(2x)-5)=0 equation:


Simplifying
(e(2x) + -3e(3x)) + -1(4e(2x) + -5) = 0

Remove parenthesis around (2x)
(e * 2x + -3e(3x)) + -1(4e(2x) + -5) = 0

Reorder the terms for easier multiplication:
(2e * x + -3e(3x)) + -1(4e(2x) + -5) = 0

Multiply e * x
(2ex + -3e(3x)) + -1(4e(2x) + -5) = 0

Remove parenthesis around (3x)
(2ex + -3e * 3x) + -1(4e(2x) + -5) = 0

Reorder the terms for easier multiplication:
(2ex + -3 * 3e * x) + -1(4e(2x) + -5) = 0

Multiply -3 * 3
(2ex + -9e * x) + -1(4e(2x) + -5) = 0

Multiply e * x
(2ex + -9ex) + -1(4e(2x) + -5) = 0

Combine like terms: 2ex + -9ex = -7ex
(-7ex) + -1(4e(2x) + -5) = 0
(-7ex) + -1(4e(2x) + -5) = 0

Remove parenthesis around (2x)
(-7ex) + -1(4e * 2x + -5) = 0

Reorder the terms for easier multiplication:
(-7ex) + -1(4 * 2e * x + -5) = 0

Multiply 4 * 2
(-7ex) + -1(8e * x + -5) = 0

Multiply e * x
(-7ex) + -1(8ex + -5) = 0

Reorder the terms:
(-7ex) + -1(-5 + 8ex) = 0
(-7ex) + (-5 * -1 + 8ex * -1) = 0
(-7ex) + (5 + -8ex) = 0

Reorder the terms:
5 + (-7ex) + -8ex = 0

Combine like terms: (-7ex) + -8ex = -15ex
5 + -15ex = 0

Solving
5 + -15ex = 0

Solving for variable 'e'.

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

Add '-5' to each side of the equation.
5 + -5 + -15ex = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -15ex = 0 + -5
-15ex = 0 + -5

Combine like terms: 0 + -5 = -5
-15ex = -5

Divide each side by '-15x'.
e = 0.3333333333x-1

Simplifying
e = 0.3333333333x-1

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