m^2+20mn+51n^2=0

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Solution for m^2+20mn+51n^2=0 equation: 


Simplifying
m2 + 20mn + 51n2 = 0

Reorder the terms:
20mn + m2 + 51n2 = 0

Solving
20mn + m2 + 51n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + 3n)(m + 17n) = 0


Subproblem 1
Set the factor '(m + 3n)' equal to zero and attempt to solve:

Simplifying
m + 3n = 0

Solving
m + 3n = 0

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

Add '-3n' to each side of the equation.
m + 3n + -3n = 0 + -3n

Combine like terms: 3n + -3n = 0
m + 0 = 0 + -3n
m = 0 + -3n
Remove the zero:
m = -3n

Simplifying
m = -3n

Subproblem 2
Set the factor '(m + 17n)' equal to zero and attempt to solve:

Simplifying
m + 17n = 0

Solving
m + 17n = 0

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

Add '-17n' to each side of the equation.
m + 17n + -17n = 0 + -17n

Combine like terms: 17n + -17n = 0
m + 0 = 0 + -17n
m = 0 + -17n
Remove the zero:
m = -17n

Simplifying
m = -17n
Solution
m = {-3n, -17n}

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