(6m-11n)(3m+2n)=0

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Solution for (6m-11n)(3m+2n)=0 equation: 


Simplifying
(6m + -11n)(3m + 2n) = 0

Multiply (6m + -11n) * (3m + 2n)
(6m * (3m + 2n) + -11n * (3m + 2n)) = 0
((3m * 6m + 2n * 6m) + -11n * (3m + 2n)) = 0

Reorder the terms:
((12mn + 18m2) + -11n * (3m + 2n)) = 0
((12mn + 18m2) + -11n * (3m + 2n)) = 0
(12mn + 18m2 + (3m * -11n + 2n * -11n)) = 0
(12mn + 18m2 + (-33mn + -22n2)) = 0

Reorder the terms:
(12mn + -33mn + 18m2 + -22n2) = 0

Combine like terms: 12mn + -33mn = -21mn
(-21mn + 18m2 + -22n2) = 0

Solving
-21mn + 18m2 + -22n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(6m + -11n)(3m + 2n) = 0


Subproblem 1
Set the factor '(6m + -11n)' equal to zero and attempt to solve:

Simplifying
6m + -11n = 0

Solving
6m + -11n = 0

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

Add '11n' to each side of the equation.
6m + -11n + 11n = 0 + 11n

Combine like terms: -11n + 11n = 0
6m + 0 = 0 + 11n
6m = 0 + 11n
Remove the zero:
6m = 11n

Divide each side by '6'.
m = 1.833333333n

Simplifying
m = 1.833333333n

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

Simplifying
3m + 2n = 0

Solving
3m + 2n = 0

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

Add '-2n' to each side of the equation.
3m + 2n + -2n = 0 + -2n

Combine like terms: 2n + -2n = 0
3m + 0 = 0 + -2n
3m = 0 + -2n
Remove the zero:
3m = -2n

Divide each side by '3'.
m = -0.6666666667n

Simplifying
m = -0.6666666667n
Solution
m = {1.833333333n, -0.6666666667n}

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