3e(x)+4e(x+2)=2e(x+9)

Solution for 3e(x)+4e(x+2)=2e(x+9) equation:

Simplifying
3e(x) + 4e(x + 2) = 2e(x + 9)

Multiply e * x
3ex + 4e(x + 2) = 2e(x + 9)

Reorder the terms:
3ex + 4e(2 + x) = 2e(x + 9)
3ex + (2 * 4e + x * 4e) = 2e(x + 9)
3ex + (8e + 4ex) = 2e(x + 9)

Reorder the terms:
8e + 3ex + 4ex = 2e(x + 9)

Combine like terms: 3ex + 4ex = 7ex
8e + 7ex = 2e(x + 9)

Reorder the terms:
8e + 7ex = 2e(9 + x)
8e + 7ex = (9 * 2e + x * 2e)
8e + 7ex = (18e + 2ex)

Solving
8e + 7ex = 18e + 2ex

Solving for variable 'e'.

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

Add '-18e' to each side of the equation.
8e + -18e + 7ex = 18e + -18e + 2ex

Combine like terms: 8e + -18e = -10e
-10e + 7ex = 18e + -18e + 2ex

Combine like terms: 18e + -18e = 0
-10e + 7ex = 0 + 2ex
-10e + 7ex = 2ex

Add '-2ex' to each side of the equation.
-10e + 7ex + -2ex = 2ex + -2ex

Combine like terms: 7ex + -2ex = 5ex
-10e + 5ex = 2ex + -2ex

Combine like terms: 2ex + -2ex = 0
-10e + 5ex = 0

Factor out the Greatest Common Factor (GCF), '5e'.
5e(-2 + x) = 0

Ignore the factor 5.
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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Add '-1x' to each side of the equation.
x + -1x = 2 + -1x

Combine like terms: x + -1x = 0
0 = 2 + -1x

Simplifying
0 = 2 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
e = {0}