(5x+1)m+(5x+3)m+(4x)m=102m

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Solution for (5x+1)m+(5x+3)m+(4x)m=102m equation: 


Simplifying
(5x + 1) * m + (5x + 3) * m + (4x) * m = 102m

Reorder the terms:
(1 + 5x) * m + (5x + 3) * m + (4x) * m = 102m

Reorder the terms for easier multiplication:
m(1 + 5x) + (5x + 3) * m + (4x) * m = 102m
(1 * m + 5x * m) + (5x + 3) * m + (4x) * m = 102m
(1m + 5mx) + (5x + 3) * m + (4x) * m = 102m

Reorder the terms:
1m + 5mx + (3 + 5x) * m + (4x) * m = 102m

Reorder the terms for easier multiplication:
1m + 5mx + m(3 + 5x) + (4x) * m = 102m
1m + 5mx + (3 * m + 5x * m) + (4x) * m = 102m
1m + 5mx + (3m + 5mx) + (4x) * m = 102m

Remove parenthesis around (4x)
1m + 5mx + 3m + 5mx + 4x * m = 102m

Multiply x * m
1m + 5mx + 3m + 5mx + 4mx = 102m

Reorder the terms:
1m + 3m + 5mx + 5mx + 4mx = 102m

Combine like terms: 1m + 3m = 4m
4m + 5mx + 5mx + 4mx = 102m

Combine like terms: 5mx + 5mx = 10mx
4m + 10mx + 4mx = 102m

Combine like terms: 10mx + 4mx = 14mx
4m + 14mx = 102m

Solving
4m + 14mx = 102m

Solving for variable 'm'.

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

Add '-102m' to each side of the equation.
4m + -102m + 14mx = 102m + -102m

Combine like terms: 4m + -102m = -98m
-98m + 14mx = 102m + -102m

Combine like terms: 102m + -102m = 0
-98m + 14mx = 0

Factor out the Greatest Common Factor (GCF), '14m'.
14m(-7 + x) = 0

Ignore the factor 14.

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 '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Add '-1x' to each side of the equation.
x + -1x = 7 + -1x

Combine like terms: x + -1x = 0
0 = 7 + -1x

Simplifying
0 = 7 + -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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