(2mn-4)(2mn-4)=

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Solution for (2mn-4)(2mn-4)= equation: 


Simplifying
(2mn + -4)(2mn + -4) = 0

Reorder the terms:
(-4 + 2mn)(2mn + -4) = 0

Reorder the terms:
(-4 + 2mn)(-4 + 2mn) = 0

Multiply (-4 + 2mn) * (-4 + 2mn)
(-4(-4 + 2mn) + 2mn * (-4 + 2mn)) = 0
((-4 * -4 + 2mn * -4) + 2mn * (-4 + 2mn)) = 0
((16 + -8mn) + 2mn * (-4 + 2mn)) = 0
(16 + -8mn + (-4 * 2mn + 2mn * 2mn)) = 0
(16 + -8mn + (-8mn + 4m2n2)) = 0

Combine like terms: -8mn + -8mn = -16mn
(16 + -16mn + 4m2n2) = 0

Solving
16 + -16mn + 4m2n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -4mn + m2n2) = 0

Factor a trinomial.
4((2 + -1mn)(2 + -1mn)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + -1mn)' equal to zero and attempt to solve:

Simplifying
2 + -1mn = 0

Solving
2 + -1mn = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1mn = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1mn = 0 + -2
-1mn = 0 + -2

Combine like terms: 0 + -2 = -2
-1mn = -2

Divide each side by '-1n'.
m = 2n-1

Simplifying
m = 2n-1

Subproblem 2
Set the factor '(2 + -1mn)' equal to zero and attempt to solve:

Simplifying
2 + -1mn = 0

Solving
2 + -1mn = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1mn = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1mn = 0 + -2
-1mn = 0 + -2

Combine like terms: 0 + -2 = -2
-1mn = -2

Divide each side by '-1n'.
m = 2n-1

Simplifying
m = 2n-1
Solution
m = {2n-1, 2n-1}

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