(5m-4n)(m-4n)=

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Solution for (5m-4n)(m-4n)= equation: 


Simplifying
(5m + -4n)(m + -4n) = 0

Multiply (5m + -4n) * (m + -4n)
(5m * (m + -4n) + -4n * (m + -4n)) = 0
((m * 5m + -4n * 5m) + -4n * (m + -4n)) = 0

Reorder the terms:
((-20mn + 5m2) + -4n * (m + -4n)) = 0
((-20mn + 5m2) + -4n * (m + -4n)) = 0
(-20mn + 5m2 + (m * -4n + -4n * -4n)) = 0
(-20mn + 5m2 + (-4mn + 16n2)) = 0

Reorder the terms:
(-20mn + -4mn + 5m2 + 16n2) = 0

Combine like terms: -20mn + -4mn = -24mn
(-24mn + 5m2 + 16n2) = 0

Solving
-24mn + 5m2 + 16n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -4n)(5m + -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 '(5m + -4n)' equal to zero and attempt to solve:

Simplifying
5m + -4n = 0

Solving
5m + -4n = 0

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

Add '4n' to each side of the equation.
5m + -4n + 4n = 0 + 4n

Combine like terms: -4n + 4n = 0
5m + 0 = 0 + 4n
5m = 0 + 4n
Remove the zero:
5m = 4n

Divide each side by '5'.
m = 0.8n

Simplifying
m = 0.8n
Solution
m = {4n, 0.8n}

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