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

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

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

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

Reorder the terms:
((16mn + 16m2) + -8n * (8m + 8n)) = 0
((16mn + 16m2) + -8n * (8m + 8n)) = 0
(16mn + 16m2 + (8m * -8n + 8n * -8n)) = 0
(16mn + 16m2 + (-64mn + -64n2)) = 0

Reorder the terms:
(16mn + -64mn + 16m2 + -64n2) = 0

Combine like terms: 16mn + -64mn = -48mn
(-48mn + 16m2 + -64n2) = 0

Solving
-48mn + 16m2 + -64n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-3mn + m2 + -4n2) = 0

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

Ignore the factor 16.
Subproblem 1
Set the factor '(m + -4n)' equal to zero and attempt to solve:

Simplifying
m + -4n = 0

Solving
m + -4n = 0

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

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

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

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

Simplifying
m + n = 0

Solving
m + n = 0

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

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

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

Simplifying
m = -1n
Solution
m = {4n, -1n}