(m-n)x+(m+n)x=10m

Solution for (m-n)x+(m+n)x=10m equation:

Simplifying
(m + -1n) * x + (m + n) * x = 10m

Reorder the terms for easier multiplication:
x(m + -1n) + (m + n) * x = 10m
(m * x + -1n * x) + (m + n) * x = 10m
(mx + -1nx) + (m + n) * x = 10m

Reorder the terms for easier multiplication:
mx + -1nx + x(m + n) = 10m
mx + -1nx + (m * x + n * x) = 10m
mx + -1nx + (mx + nx) = 10m

Reorder the terms:
mx + mx + -1nx + nx = 10m

Combine like terms: mx + mx = 2mx
2mx + -1nx + nx = 10m

Combine like terms: -1nx + nx = 0
2mx + 0 = 10m
2mx = 10m

Solving
2mx = 10m

Solving for variable 'm'.

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

Add '-10m' to each side of the equation.
-10m + 2mx = 10m + -10m

Combine like terms: 10m + -10m = 0
-10m + 2mx = 0

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

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

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

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

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

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

Add '-1x' to each side of the equation.
x + -1x = 5 + -1x

Combine like terms: x + -1x = 0
0 = 5 + -1x

Simplifying
0 = 5 + -1x

The solution to this equation could not be determined.

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