(2x-6)m=(x+3)m

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Solution for (2x-6)m=(x+3)m equation: 


Simplifying
(2x + -6) * m = (x + 3) * m

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

Reorder the terms for easier multiplication:
m(-6 + 2x) = (x + 3) * m
(-6 * m + 2x * m) = (x + 3) * m
(-6m + 2mx) = (x + 3) * m

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

Reorder the terms for easier multiplication:
-6m + 2mx = m(3 + x)
-6m + 2mx = (3 * m + x * m)
-6m + 2mx = (3m + mx)

Solving
-6m + 2mx = 3m + mx

Solving for variable 'm'.

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

Add '-3m' to each side of the equation.
-6m + -3m + 2mx = 3m + -3m + mx

Combine like terms: -6m + -3m = -9m
-9m + 2mx = 3m + -3m + mx

Combine like terms: 3m + -3m = 0
-9m + 2mx = 0 + mx
-9m + 2mx = mx

Add '-1mx' to each side of the equation.
-9m + 2mx + -1mx = mx + -1mx

Combine like terms: 2mx + -1mx = 1mx
-9m + 1mx = mx + -1mx

Combine like terms: mx + -1mx = 0
-9m + 1mx = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-9 + x) = 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 '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Add '-1x' to each side of the equation.
x + -1x = 9 + -1x

Combine like terms: x + -1x = 0
0 = 9 + -1x

Simplifying
0 = 9 + -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}

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