4mn(m-n)+6=8m(2m-n)+4

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Solution for 4mn(m-n)+6=8m(2m-n)+4 equation: 


Simplifying
4mn(m + -1n) + 6 = 8m(2m + -1n) + 4
(m * 4mn + -1n * 4mn) + 6 = 8m(2m + -1n) + 4

Reorder the terms:
(-4mn2 + 4m2n) + 6 = 8m(2m + -1n) + 4
(-4mn2 + 4m2n) + 6 = 8m(2m + -1n) + 4

Reorder the terms:
6 + -4mn2 + 4m2n = 8m(2m + -1n) + 4
6 + -4mn2 + 4m2n = (2m * 8m + -1n * 8m) + 4

Reorder the terms:
6 + -4mn2 + 4m2n = (-8mn + 16m2) + 4
6 + -4mn2 + 4m2n = (-8mn + 16m2) + 4

Reorder the terms:
6 + -4mn2 + 4m2n = 4 + -8mn + 16m2

Solving
6 + -4mn2 + 4m2n = 4 + -8mn + 16m2

Solving for variable 'm'.

Reorder the terms:
6 + -4 + 8mn + -4mn2 + -16m2 + 4m2n = 4 + -8mn + 16m2 + -4 + 8mn + -16m2

Combine like terms: 6 + -4 = 2
2 + 8mn + -4mn2 + -16m2 + 4m2n = 4 + -8mn + 16m2 + -4 + 8mn + -16m2

Reorder the terms:
2 + 8mn + -4mn2 + -16m2 + 4m2n = 4 + -4 + -8mn + 8mn + 16m2 + -16m2

Combine like terms: 4 + -4 = 0
2 + 8mn + -4mn2 + -16m2 + 4m2n = 0 + -8mn + 8mn + 16m2 + -16m2
2 + 8mn + -4mn2 + -16m2 + 4m2n = -8mn + 8mn + 16m2 + -16m2

Combine like terms: -8mn + 8mn = 0
2 + 8mn + -4mn2 + -16m2 + 4m2n = 0 + 16m2 + -16m2
2 + 8mn + -4mn2 + -16m2 + 4m2n = 16m2 + -16m2

Combine like terms: 16m2 + -16m2 = 0
2 + 8mn + -4mn2 + -16m2 + 4m2n = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 4mn + -2mn2 + -8m2 + 2m2n) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 4mn + -2mn2 + -8m2 + 2m2n)' equal to zero and attempt to solve:

Simplifying
1 + 4mn + -2mn2 + -8m2 + 2m2n = 0

Solving
1 + 4mn + -2mn2 + -8m2 + 2m2n = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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