7m(2x+y)+3m(y-4x)=

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Solution for 7m(2x+y)+3m(y-4x)= equation: 


Simplifying
7m(2x + y) + 3m(y + -4x) = 0
(2x * 7m + y * 7m) + 3m(y + -4x) = 0
(14mx + 7my) + 3m(y + -4x) = 0

Reorder the terms:
14mx + 7my + 3m(-4x + y) = 0
14mx + 7my + (-4x * 3m + y * 3m) = 0
14mx + 7my + (-12mx + 3my) = 0

Reorder the terms:
14mx + -12mx + 7my + 3my = 0

Combine like terms: 14mx + -12mx = 2mx
2mx + 7my + 3my = 0

Combine like terms: 7my + 3my = 10my
2mx + 10my = 0

Solving
2mx + 10my = 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), '2m'.
2m(x + 5y) = 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 '(x + 5y)' equal to zero and attempt to solve:

Simplifying
x + 5y = 0

Solving
x + 5y = 0

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

Add '-1x' to each side of the equation.
x + -1x + 5y = 0 + -1x

Combine like terms: x + -1x = 0
0 + 5y = 0 + -1x
5y = 0 + -1x
Remove the zero:
5y = -1x

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

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

Simplifying
0 = -1x + -5y

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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