-[-(7mn+5m)+(-3m)(m+2)]=0

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Solution for -[-(7mn+5m)+(-3m)(m+2)]=0 equation: 


Simplifying
-1[-1(7mn + 5m) + (-3m)(m + 2)] = 0

Reorder the terms:
-1[-1(5m + 7mn) + (-3m)(m + 2)] = 0
-1[(5m * -1 + 7mn * -1) + (-3m)(m + 2)] = 0
-1[(-5m + -7mn) + (-3m)(m + 2)] = 0

Remove parenthesis around (-3m)
-1[-5m + -7mn + -3m(m + 2)] = 0

Reorder the terms:
-1[-5m + -7mn + -3m(2 + m)] = 0
-1[-5m + -7mn + (2 * -3m + m * -3m)] = 0
-1[-5m + -7mn + (-6m + -3m2)] = 0

Reorder the terms:
-1[-5m + -6m + -7mn + -3m2] = 0

Combine like terms: -5m + -6m = -11m
-1[-11m + -7mn + -3m2] = 0
[-11m * -1 + -7mn * -1 + -3m2 * -1] = 0
[11m + 7mn + 3m2] = 0

Solving
11m + 7mn + 3m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm'.
m(11 + 7n + 3m) = 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 '(11 + 7n + 3m)' equal to zero and attempt to solve:

Simplifying
11 + 7n + 3m = 0

Reorder the terms:
11 + 3m + 7n = 0

Solving
11 + 3m + 7n = 0

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

Add '-11' to each side of the equation.
11 + 3m + -11 + 7n = 0 + -11

Reorder the terms:
11 + -11 + 3m + 7n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 3m + 7n = 0 + -11
3m + 7n = 0 + -11

Combine like terms: 0 + -11 = -11
3m + 7n = -11

Add '-7n' to each side of the equation.
3m + 7n + -7n = -11 + -7n

Combine like terms: 7n + -7n = 0
3m + 0 = -11 + -7n
3m = -11 + -7n

Divide each side by '3'.
m = -3.666666667 + -2.333333333n

Simplifying
m = -3.666666667 + -2.333333333n
Solution
m = {0, -3.666666667 + -2.333333333n}

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