0=9m^2-30mn+25n^2

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Solution for 0=9m^2-30mn+25n^2 equation: 


Simplifying
0 = 9m2 + -30mn + 25n2

Reorder the terms:
0 = -30mn + 9m2 + 25n2

Solving
0 = -30mn + 9m2 + 25n2

Solving for variable 'm'.
Remove the zero:
30mn + -9m2 + -25n2 = -30mn + 9m2 + 25n2 + 30mn + -9m2 + -25n2

Reorder the terms:
30mn + -9m2 + -25n2 = -30mn + 30mn + 9m2 + -9m2 + 25n2 + -25n2

Combine like terms: -30mn + 30mn = 0
30mn + -9m2 + -25n2 = 0 + 9m2 + -9m2 + 25n2 + -25n2
30mn + -9m2 + -25n2 = 9m2 + -9m2 + 25n2 + -25n2

Combine like terms: 9m2 + -9m2 = 0
30mn + -9m2 + -25n2 = 0 + 25n2 + -25n2
30mn + -9m2 + -25n2 = 25n2 + -25n2

Combine like terms: 25n2 + -25n2 = 0
30mn + -9m2 + -25n2 = 0

Factor a trinomial.
(-3m + 5n)(3m + -5n) = 0


Subproblem 1
Set the factor '(-3m + 5n)' equal to zero and attempt to solve:

Simplifying
-3m + 5n = 0

Solving
-3m + 5n = 0

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

Add '-5n' to each side of the equation.
-3m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
-3m + 0 = 0 + -5n
-3m = 0 + -5n
Remove the zero:
-3m = -5n

Divide each side by '-3'.
m = 1.666666667n

Simplifying
m = 1.666666667n

Subproblem 2
Set the factor '(3m + -5n)' equal to zero and attempt to solve:

Simplifying
3m + -5n = 0

Solving
3m + -5n = 0

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

Add '5n' to each side of the equation.
3m + -5n + 5n = 0 + 5n

Combine like terms: -5n + 5n = 0
3m + 0 = 0 + 5n
3m = 0 + 5n
Remove the zero:
3m = 5n

Divide each side by '3'.
m = 1.666666667n

Simplifying
m = 1.666666667n
Solution
m = {1.666666667n, 1.666666667n}

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