6m^2-13mn-5n^2=0

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Solution for 6m^2-13mn-5n^2=0 equation: 


Simplifying
6m2 + -13mn + -5n2 = 0

Reorder the terms:
-13mn + 6m2 + -5n2 = 0

Solving
-13mn + 6m2 + -5n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2m + -5n)(3m + n) = 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 '(3m + n)' equal to zero and attempt to solve:

Simplifying
3m + n = 0

Solving
3m + n = 0

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

Add '-1n' to each side of the equation.
3m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
3m + 0 = 0 + -1n
3m = 0 + -1n
Remove the zero:
3m = -1n

Divide each side by '3'.
m = -0.3333333333n

Simplifying
m = -0.3333333333n
Solution
m = {2.5n, -0.3333333333n}

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