8n^2-6mn-5m^2=0

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Solution for 8n^2-6mn-5m^2=0 equation: 


Simplifying
8n2 + -6mn + -5m2 = 0

Reorder the terms:
-6mn + -5m2 + 8n2 = 0

Solving
-6mn + -5m2 + 8n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-1m + -2n)(5m + -4n) = 0


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

Simplifying
-1m + -2n = 0

Solving
-1m + -2n = 0

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

Add '2n' to each side of the equation.
-1m + -2n + 2n = 0 + 2n

Combine like terms: -2n + 2n = 0
-1m + 0 = 0 + 2n
-1m = 0 + 2n
Remove the zero:
-1m = 2n

Divide each side by '-1'.
m = -2n

Simplifying
m = -2n

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 = {-2n, 0.8n}

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