(x+3)m+2xm+(x+3)m+2xm=

Solution for (x+3)m+2xm+(x+3)m+2xm= equation:

Simplifying
(x + 3) * m + 2xm + (x + 3) * m + 2xm = 0

Reorder the terms:
(3 + x) * m + 2xm + (x + 3) * m + 2xm = 0

Reorder the terms for easier multiplication:
m(3 + x) + 2xm + (x + 3) * m + 2xm = 0
(3 * m + x * m) + 2xm + (x + 3) * m + 2xm = 0
(3m + mx) + 2xm + (x + 3) * m + 2xm = 0

Reorder the terms:
3m + mx + 2mx + (3 + x) * m + 2xm = 0

Reorder the terms for easier multiplication:
3m + mx + 2mx + m(3 + x) + 2xm = 0
3m + mx + 2mx + (3 * m + x * m) + 2xm = 0
3m + mx + 2mx + (3m + mx) + 2xm = 0

Reorder the terms:
3m + 3m + mx + 2mx + mx + 2mx = 0

Combine like terms: 3m + 3m = 6m
6m + mx + 2mx + mx + 2mx = 0

Combine like terms: mx + 2mx = 3mx
6m + 3mx + mx + 2mx = 0

Combine like terms: 3mx + mx = 4mx
6m + 4mx + 2mx = 0

Combine like terms: 4mx + 2mx = 6mx
6m + 6mx = 0

Solving
6m + 6mx = 0

Solving for variable 'm'.

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

Factor out the Greatest Common Factor (GCF), '6m'.
6m(1 + x) = 0

Ignore the factor 6.
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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + -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}