6m^2+11mn+3n^2=0

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Solution for 6m^2+11mn+3n^2=0 equation:


Simplifying
6m2 + 11mn + 3n2 = 0

Reorder the terms:
11mn + 6m2 + 3n2 = 0

Solving
11mn + 6m2 + 3n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(3m + n)(2m + 3n) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(2m + 3n)' equal to zero and attempt to solve: Simplifying 2m + 3n = 0 Solving 2m + 3n = 0 Move all terms containing m to the left, all other terms to the right. Add '-3n' to each side of the equation. 2m + 3n + -3n = 0 + -3n Combine like terms: 3n + -3n = 0 2m + 0 = 0 + -3n 2m = 0 + -3n Remove the zero: 2m = -3n Divide each side by '2'. m = -1.5n Simplifying m = -1.5n

Solution

m = {-0.3333333333n, -1.5n}

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