(2m+5n)(2m+5n)=

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Solution for (2m+5n)(2m+5n)= equation: 


Simplifying
(2m + 5n)(2m + 5n) = 0

Multiply (2m + 5n) * (2m + 5n)
(2m * (2m + 5n) + 5n * (2m + 5n)) = 0
((2m * 2m + 5n * 2m) + 5n * (2m + 5n)) = 0

Reorder the terms:
((10mn + 4m2) + 5n * (2m + 5n)) = 0
((10mn + 4m2) + 5n * (2m + 5n)) = 0
(10mn + 4m2 + (2m * 5n + 5n * 5n)) = 0
(10mn + 4m2 + (10mn + 25n2)) = 0

Reorder the terms:
(10mn + 10mn + 4m2 + 25n2) = 0

Combine like terms: 10mn + 10mn = 20mn
(20mn + 4m2 + 25n2) = 0

Solving
20mn + 4m2 + 25n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2m + 5n)(2m + 5n) = 0


Subproblem 1
Set the factor '(2m + 5n)' equal to zero and attempt to solve:

Simplifying
2m + 5n = 0

Solving
2m + 5n = 0

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

Add '-5n' to each side of the equation.
2m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
2m + 0 = 0 + -5n
2m = 0 + -5n
Remove the zero:
2m = -5n

Divide each side by '2'.
m = -2.5n

Simplifying
m = -2.5n

Subproblem 2
Set the factor '(2m + 5n)' equal to zero and attempt to solve:

Simplifying
2m + 5n = 0

Solving
2m + 5n = 0

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

Add '-5n' to each side of the equation.
2m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
2m + 0 = 0 + -5n
2m = 0 + -5n
Remove the zero:
2m = -5n

Divide each side by '2'.
m = -2.5n

Simplifying
m = -2.5n
Solution
m = {-2.5n, -2.5n}

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