m(n-x)-m(n-1)=m(mx-a)

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Solution for m(n-x)-m(n-1)=m(mx-a) equation: 


Simplifying
m(n + -1x) + -1m(n + -1) = m(mx + -1a)
(n * m + -1x * m) + -1m(n + -1) = m(mx + -1a)
(mn + -1mx) + -1m(n + -1) = m(mx + -1a)

Reorder the terms:
mn + -1mx + -1m(-1 + n) = m(mx + -1a)
mn + -1mx + (-1 * -1m + n * -1m) = m(mx + -1a)
mn + -1mx + (1m + -1mn) = m(mx + -1a)

Reorder the terms:
1m + mn + -1mn + -1mx = m(mx + -1a)

Combine like terms: mn + -1mn = 0
1m + 0 + -1mx = m(mx + -1a)
1m + -1mx = m(mx + -1a)

Reorder the terms:
1m + -1mx = m(-1a + mx)
1m + -1mx = (-1a * m + mx * m)
1m + -1mx = (-1am + m2x)

Solving
1m + -1mx = -1am + m2x

Solving for variable 'm'.

Reorder the terms:
am + 1m + -1mx + -1m2x = -1am + m2x + am + -1m2x

Reorder the terms:
am + 1m + -1mx + -1m2x = -1am + am + m2x + -1m2x

Combine like terms: -1am + am = 0
am + 1m + -1mx + -1m2x = 0 + m2x + -1m2x
am + 1m + -1mx + -1m2x = m2x + -1m2x

Combine like terms: m2x + -1m2x = 0
am + 1m + -1mx + -1m2x = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(a + 1 + -1x + -1mx) = 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 '(a + 1 + -1x + -1mx)' equal to zero and attempt to solve:

Simplifying
a + 1 + -1x + -1mx = 0

Reorder the terms:
1 + a + -1mx + -1x = 0

Solving
1 + a + -1mx + -1x = 0

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

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

Reorder the terms:
1 + -1 + a + -1mx + -1x = 0 + -1

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

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

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

Reorder the terms:
a + -1a + -1mx + -1x = -1 + -1a

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

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

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

Divide each side by '-1x'.
m = x-1 + ax-1 + -1

Simplifying
m = x-1 + ax-1 + -1

Reorder the terms:
m = -1 + ax-1 + x-1
Solution
m = {0, -1 + ax-1 + x-1}

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