m(m+6n-6k)+-n(m+6n-6k)+(m+6n-6k)=

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Solution for m(m+6n-6k)+-n(m+6n-6k)+(m+6n-6k)= equation: 


Simplifying
m(m + 6n + -6k) + -1n(m + 6n + -6k) + (m + 6n + -6k) = 0

Reorder the terms:
m(-6k + m + 6n) + -1n(m + 6n + -6k) + (m + 6n + -6k) = 0
(-6k * m + m * m + 6n * m) + -1n(m + 6n + -6k) + (m + 6n + -6k) = 0

Reorder the terms:
(-6km + 6mn + m2) + -1n(m + 6n + -6k) + (m + 6n + -6k) = 0
(-6km + 6mn + m2) + -1n(m + 6n + -6k) + (m + 6n + -6k) = 0

Reorder the terms:
-6km + 6mn + m2 + -1n(-6k + m + 6n) + (m + 6n + -6k) = 0
-6km + 6mn + m2 + (-6k * -1n + m * -1n + 6n * -1n) + (m + 6n + -6k) = 0
-6km + 6mn + m2 + (6kn + -1mn + -6n2) + (m + 6n + -6k) = 0

Reorder the terms:
-6km + 6mn + m2 + 6kn + -1mn + -6n2 + (-6k + m + 6n) = 0

Remove parenthesis around (-6k + m + 6n)
-6km + 6mn + m2 + 6kn + -1mn + -6n2 + -6k + m + 6n = 0

Reorder the terms:
-6k + -6km + 6kn + m + 6mn + -1mn + m2 + 6n + -6n2 = 0

Combine like terms: 6mn + -1mn = 5mn
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = 0

Solving
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = 0

Solving for variable 'k'.

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

Add '-1m' to each side of the equation.
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -1m + -6n2 = 0 + -1m

Reorder the terms:
-6k + -6km + 6kn + m + -1m + 5mn + m2 + 6n + -6n2 = 0 + -1m

Combine like terms: m + -1m = 0
-6k + -6km + 6kn + 0 + 5mn + m2 + 6n + -6n2 = 0 + -1m
-6k + -6km + 6kn + 5mn + m2 + 6n + -6n2 = 0 + -1m
Remove the zero:
-6k + -6km + 6kn + 5mn + m2 + 6n + -6n2 = -1m

Add '-5mn' to each side of the equation.
-6k + -6km + 6kn + 5mn + m2 + 6n + -5mn + -6n2 = -1m + -5mn

Reorder the terms:
-6k + -6km + 6kn + 5mn + -5mn + m2 + 6n + -6n2 = -1m + -5mn

Combine like terms: 5mn + -5mn = 0
-6k + -6km + 6kn + 0 + m2 + 6n + -6n2 = -1m + -5mn
-6k + -6km + 6kn + m2 + 6n + -6n2 = -1m + -5mn

Add '-1m2' to each side of the equation.
-6k + -6km + 6kn + m2 + 6n + -1m2 + -6n2 = -1m + -5mn + -1m2

Reorder the terms:
-6k + -6km + 6kn + m2 + -1m2 + 6n + -6n2 = -1m + -5mn + -1m2

Combine like terms: m2 + -1m2 = 0
-6k + -6km + 6kn + 0 + 6n + -6n2 = -1m + -5mn + -1m2
-6k + -6km + 6kn + 6n + -6n2 = -1m + -5mn + -1m2

Add '-6n' to each side of the equation.
-6k + -6km + 6kn + 6n + -6n + -6n2 = -1m + -5mn + -1m2 + -6n

Combine like terms: 6n + -6n = 0
-6k + -6km + 6kn + 0 + -6n2 = -1m + -5mn + -1m2 + -6n
-6k + -6km + 6kn + -6n2 = -1m + -5mn + -1m2 + -6n

Add '6n2' to each side of the equation.
-6k + -6km + 6kn + -6n2 + 6n2 = -1m + -5mn + -1m2 + -6n + 6n2

Combine like terms: -6n2 + 6n2 = 0
-6k + -6km + 6kn + 0 = -1m + -5mn + -1m2 + -6n + 6n2
-6k + -6km + 6kn = -1m + -5mn + -1m2 + -6n + 6n2

Reorder the terms:
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = -1m + m + -5mn + 5mn + -1m2 + m2 + -6n + 6n + 6n2 + -6n2

Combine like terms: -1m + m = 0
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = 0 + -5mn + 5mn + -1m2 + m2 + -6n + 6n + 6n2 + -6n2
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = -5mn + 5mn + -1m2 + m2 + -6n + 6n + 6n2 + -6n2

Combine like terms: -5mn + 5mn = 0
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = 0 + -1m2 + m2 + -6n + 6n + 6n2 + -6n2
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = -1m2 + m2 + -6n + 6n + 6n2 + -6n2

Combine like terms: -1m2 + m2 = 0
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = 0 + -6n + 6n + 6n2 + -6n2
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = -6n + 6n + 6n2 + -6n2

Combine like terms: -6n + 6n = 0
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = 0 + 6n2 + -6n2
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
-6k + -6km + 6kn + m + 5mn + m2 + 6n + -6n2 = 0

The solution to this equation could not be determined.

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