3m(x-2)+4mx=2m(x+1)

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Solution for 3m(x-2)+4mx=2m(x+1) equation: 


Simplifying
3m(x + -2) + 4mx = 2m(x + 1)

Reorder the terms:
3m(-2 + x) + 4mx = 2m(x + 1)
(-2 * 3m + x * 3m) + 4mx = 2m(x + 1)
(-6m + 3mx) + 4mx = 2m(x + 1)

Combine like terms: 3mx + 4mx = 7mx
-6m + 7mx = 2m(x + 1)

Reorder the terms:
-6m + 7mx = 2m(1 + x)
-6m + 7mx = (1 * 2m + x * 2m)
-6m + 7mx = (2m + 2mx)

Solving
-6m + 7mx = 2m + 2mx

Solving for variable 'm'.

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

Add '-2m' to each side of the equation.
-6m + -2m + 7mx = 2m + -2m + 2mx

Combine like terms: -6m + -2m = -8m
-8m + 7mx = 2m + -2m + 2mx

Combine like terms: 2m + -2m = 0
-8m + 7mx = 0 + 2mx
-8m + 7mx = 2mx

Add '-2mx' to each side of the equation.
-8m + 7mx + -2mx = 2mx + -2mx

Combine like terms: 7mx + -2mx = 5mx
-8m + 5mx = 2mx + -2mx

Combine like terms: 2mx + -2mx = 0
-8m + 5mx = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-8 + 5x) = 0


Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0

Subproblem 2
Set the factor '(-8 + 5x)' equal to zero and attempt to solve:

Simplifying
-8 + 5x = 0

Solving
-8 + 5x = 0

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

Add '8' to each side of the equation.
-8 + 8 + 5x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 5x = 0 + 8
5x = 0 + 8

Combine like terms: 0 + 8 = 8
5x = 8

Add '-5x' to each side of the equation.
5x + -5x = 8 + -5x

Combine like terms: 5x + -5x = 0
0 = 8 + -5x

Simplifying
0 = 8 + -5x

The solution to this equation could not be determined.

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

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