(m-n+k)(m+5n-4K)=

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Solution for (m-n+k)(m+5n-4K)= equation: 


Simplifying
(m + -1n + k)(m + 5n + -4K) = 0

Reorder the terms:
(k + m + -1n)(m + 5n + -4K) = 0

Reorder the terms:
(k + m + -1n)(-4K + m + 5n) = 0

Multiply (k + m + -1n) * (-4K + m + 5n)
(k(-4K + m + 5n) + m(-4K + m + 5n) + -1n * (-4K + m + 5n)) = 0
((-4K * k + m * k + 5n * k) + m(-4K + m + 5n) + -1n * (-4K + m + 5n)) = 0
((-4kK + km + 5kn) + m(-4K + m + 5n) + -1n * (-4K + m + 5n)) = 0
(-4kK + km + 5kn + (-4K * m + m * m + 5n * m) + -1n * (-4K + m + 5n)) = 0

Reorder the terms:
(-4kK + km + 5kn + (-4mK + 5mn + m2) + -1n * (-4K + m + 5n)) = 0
(-4kK + km + 5kn + (-4mK + 5mn + m2) + -1n * (-4K + m + 5n)) = 0
(-4kK + km + 5kn + -4mK + 5mn + m2 + (-4K * -1n + m * -1n + 5n * -1n)) = 0

Reorder the terms:
(-4kK + km + 5kn + -4mK + 5mn + m2 + (-1mn + 4nK + -5n2)) = 0
(-4kK + km + 5kn + -4mK + 5mn + m2 + (-1mn + 4nK + -5n2)) = 0

Reorder the terms:
(-4kK + km + 5kn + -4mK + 5mn + -1mn + m2 + 4nK + -5n2) = 0

Combine like terms: 5mn + -1mn = 4mn
(-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2) = 0

Solving
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = 0

Solving for variable 'k'.

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

Add '4mK' to each side of the equation.
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + 4mK + -5n2 = 0 + 4mK

Reorder the terms:
-4kK + km + 5kn + -4mK + 4mK + 4mn + m2 + 4nK + -5n2 = 0 + 4mK

Combine like terms: -4mK + 4mK = 0
-4kK + km + 5kn + 0 + 4mn + m2 + 4nK + -5n2 = 0 + 4mK
-4kK + km + 5kn + 4mn + m2 + 4nK + -5n2 = 0 + 4mK
Remove the zero:
-4kK + km + 5kn + 4mn + m2 + 4nK + -5n2 = 4mK

Add '-4mn' to each side of the equation.
-4kK + km + 5kn + 4mn + m2 + 4nK + -4mn + -5n2 = 4mK + -4mn

Reorder the terms:
-4kK + km + 5kn + 4mn + -4mn + m2 + 4nK + -5n2 = 4mK + -4mn

Combine like terms: 4mn + -4mn = 0
-4kK + km + 5kn + 0 + m2 + 4nK + -5n2 = 4mK + -4mn
-4kK + km + 5kn + m2 + 4nK + -5n2 = 4mK + -4mn

Add '-1m2' to each side of the equation.
-4kK + km + 5kn + m2 + 4nK + -1m2 + -5n2 = 4mK + -4mn + -1m2

Reorder the terms:
-4kK + km + 5kn + m2 + -1m2 + 4nK + -5n2 = 4mK + -4mn + -1m2

Combine like terms: m2 + -1m2 = 0
-4kK + km + 5kn + 0 + 4nK + -5n2 = 4mK + -4mn + -1m2
-4kK + km + 5kn + 4nK + -5n2 = 4mK + -4mn + -1m2

Add '-4nK' to each side of the equation.
-4kK + km + 5kn + 4nK + -4nK + -5n2 = 4mK + -4mn + -1m2 + -4nK

Combine like terms: 4nK + -4nK = 0
-4kK + km + 5kn + 0 + -5n2 = 4mK + -4mn + -1m2 + -4nK
-4kK + km + 5kn + -5n2 = 4mK + -4mn + -1m2 + -4nK

Add '5n2' to each side of the equation.
-4kK + km + 5kn + -5n2 + 5n2 = 4mK + -4mn + -1m2 + -4nK + 5n2

Combine like terms: -5n2 + 5n2 = 0
-4kK + km + 5kn + 0 = 4mK + -4mn + -1m2 + -4nK + 5n2
-4kK + km + 5kn = 4mK + -4mn + -1m2 + -4nK + 5n2

Reorder the terms:
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = 4mK + -4mK + -4mn + 4mn + -1m2 + m2 + -4nK + 4nK + 5n2 + -5n2

Combine like terms: 4mK + -4mK = 0
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = 0 + -4mn + 4mn + -1m2 + m2 + -4nK + 4nK + 5n2 + -5n2
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = -4mn + 4mn + -1m2 + m2 + -4nK + 4nK + 5n2 + -5n2

Combine like terms: -4mn + 4mn = 0
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = 0 + -1m2 + m2 + -4nK + 4nK + 5n2 + -5n2
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = -1m2 + m2 + -4nK + 4nK + 5n2 + -5n2

Combine like terms: -1m2 + m2 = 0
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = 0 + -4nK + 4nK + 5n2 + -5n2
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = -4nK + 4nK + 5n2 + -5n2

Combine like terms: -4nK + 4nK = 0
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = 0 + 5n2 + -5n2
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = 5n2 + -5n2

Combine like terms: 5n2 + -5n2 = 0
-4kK + km + 5kn + -4mK + 4mn + m2 + 4nK + -5n2 = 0

The solution to this equation could not be determined.

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