(m-n+k)(m+7n-5k)=0

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Solution for (m-n+k)(m+7n-5k)=0 equation: 


Simplifying
(m + -1n + k)(m + 7n + -5k) = 0

Reorder the terms:
(k + m + -1n)(m + 7n + -5k) = 0

Reorder the terms:
(k + m + -1n)(-5k + m + 7n) = 0

Multiply (k + m + -1n) * (-5k + m + 7n)
(k(-5k + m + 7n) + m(-5k + m + 7n) + -1n * (-5k + m + 7n)) = 0
((-5k * k + m * k + 7n * k) + m(-5k + m + 7n) + -1n * (-5k + m + 7n)) = 0

Reorder the terms:
((km + 7kn + -5k2) + m(-5k + m + 7n) + -1n * (-5k + m + 7n)) = 0
((km + 7kn + -5k2) + m(-5k + m + 7n) + -1n * (-5k + m + 7n)) = 0
(km + 7kn + -5k2 + (-5k * m + m * m + 7n * m) + -1n * (-5k + m + 7n)) = 0

Reorder the terms:
(km + 7kn + -5k2 + (-5km + 7mn + m2) + -1n * (-5k + m + 7n)) = 0
(km + 7kn + -5k2 + (-5km + 7mn + m2) + -1n * (-5k + m + 7n)) = 0
(km + 7kn + -5k2 + -5km + 7mn + m2 + (-5k * -1n + m * -1n + 7n * -1n)) = 0
(km + 7kn + -5k2 + -5km + 7mn + m2 + (5kn + -1mn + -7n2)) = 0

Reorder the terms:
(km + -5km + 7kn + 5kn + -5k2 + 7mn + -1mn + m2 + -7n2) = 0

Combine like terms: km + -5km = -4km
(-4km + 7kn + 5kn + -5k2 + 7mn + -1mn + m2 + -7n2) = 0

Combine like terms: 7kn + 5kn = 12kn
(-4km + 12kn + -5k2 + 7mn + -1mn + m2 + -7n2) = 0

Combine like terms: 7mn + -1mn = 6mn
(-4km + 12kn + -5k2 + 6mn + m2 + -7n2) = 0

Solving
-4km + 12kn + -5k2 + 6mn + m2 + -7n2 = 0

Solving for variable 'k'.

The solution to this equation could not be determined.

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