12m^2-19mn-21n^2=0

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Solution for 12m^2-19mn-21n^2=0 equation: 


Simplifying
12m2 + -19mn + -21n2 = 0

Reorder the terms:
-19mn + 12m2 + -21n2 = 0

Solving
-19mn + 12m2 + -21n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(3m + -7n)(4m + 3n) = 0


Subproblem 1
Set the factor '(3m + -7n)' equal to zero and attempt to solve:

Simplifying
3m + -7n = 0

Solving
3m + -7n = 0

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

Add '7n' to each side of the equation.
3m + -7n + 7n = 0 + 7n

Combine like terms: -7n + 7n = 0
3m + 0 = 0 + 7n
3m = 0 + 7n
Remove the zero:
3m = 7n

Divide each side by '3'.
m = 2.333333333n

Simplifying
m = 2.333333333n

Subproblem 2
Set the factor '(4m + 3n)' equal to zero and attempt to solve:

Simplifying
4m + 3n = 0

Solving
4m + 3n = 0

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

Add '-3n' to each side of the equation.
4m + 3n + -3n = 0 + -3n

Combine like terms: 3n + -3n = 0
4m + 0 = 0 + -3n
4m = 0 + -3n
Remove the zero:
4m = -3n

Divide each side by '4'.
m = -0.75n

Simplifying
m = -0.75n
Solution
m = {2.333333333n, -0.75n}

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