(m+4n)(m+4n)=

Solution for (m+4n)(m+4n)= equation:

Simplifying
(m + 4n)(m + 4n) = 0

Multiply (m + 4n) * (m + 4n)
(m(m + 4n) + 4n * (m + 4n)) = 0
((m * m + 4n * m) + 4n * (m + 4n)) = 0

Reorder the terms:
((4mn + m2) + 4n * (m + 4n)) = 0
((4mn + m2) + 4n * (m + 4n)) = 0
(4mn + m2 + (m * 4n + 4n * 4n)) = 0
(4mn + m2 + (4mn + 16n2)) = 0

Reorder the terms:
(4mn + 4mn + m2 + 16n2) = 0

Combine like terms: 4mn + 4mn = 8mn
(8mn + m2 + 16n2) = 0

Solving
8mn + m2 + 16n2 = 0

Solving for variable 'm'.

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

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 + 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
Solution
m = {-4n, -4n}