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

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


Simplifying
(8m + 2n)(4m + -4n) = 0

Multiply (8m + 2n) * (4m + -4n)
(8m * (4m + -4n) + 2n * (4m + -4n)) = 0
((4m * 8m + -4n * 8m) + 2n * (4m + -4n)) = 0

Reorder the terms:
((-32mn + 32m2) + 2n * (4m + -4n)) = 0
((-32mn + 32m2) + 2n * (4m + -4n)) = 0
(-32mn + 32m2 + (4m * 2n + -4n * 2n)) = 0
(-32mn + 32m2 + (8mn + -8n2)) = 0

Reorder the terms:
(-32mn + 8mn + 32m2 + -8n2) = 0

Combine like terms: -32mn + 8mn = -24mn
(-24mn + 32m2 + -8n2) = 0

Solving
-24mn + 32m2 + -8n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-3mn + 4m2 + -1n2) = 0

Factor a trinomial.
8((m + -1n)(4m + n)) = 0

Ignore the factor 8.

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

Simplifying
m + -1n = 0

Solving
m + -1n = 0

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

Add 'n' to each side of the equation.
m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
m + 0 = 0 + n
m = 0 + n
Remove the zero:
m = n

Simplifying
m = n

Subproblem 2
Set the factor '(4m + n)' equal to zero and attempt to solve:

Simplifying
4m + n = 0

Solving
4m + n = 0

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

Add '-1n' to each side of the equation.
4m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
4m + 0 = 0 + -1n
4m = 0 + -1n
Remove the zero:
4m = -1n

Divide each side by '4'.
m = -0.25n

Simplifying
m = -0.25n
Solution
m = {n, -0.25n}

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