(12m-2n)(7m+11n)=

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Solution for (12m-2n)(7m+11n)= equation: 


Simplifying
(12m + -2n)(7m + 11n) = 0

Multiply (12m + -2n) * (7m + 11n)
(12m * (7m + 11n) + -2n * (7m + 11n)) = 0
((7m * 12m + 11n * 12m) + -2n * (7m + 11n)) = 0

Reorder the terms:
((132mn + 84m2) + -2n * (7m + 11n)) = 0
((132mn + 84m2) + -2n * (7m + 11n)) = 0
(132mn + 84m2 + (7m * -2n + 11n * -2n)) = 0
(132mn + 84m2 + (-14mn + -22n2)) = 0

Reorder the terms:
(132mn + -14mn + 84m2 + -22n2) = 0

Combine like terms: 132mn + -14mn = 118mn
(118mn + 84m2 + -22n2) = 0

Solving
118mn + 84m2 + -22n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(59mn + 42m2 + -11n2) = 0

Factor a trinomial.
2((6m + -1n)(7m + 11n)) = 0

Ignore the factor 2.

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

Simplifying
6m + -1n = 0

Solving
6m + -1n = 0

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

Add 'n' to each side of the equation.
6m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
6m + 0 = 0 + n
6m = 0 + n
Remove the zero:
6m = n

Divide each side by '6'.
m = 0.1666666667n

Simplifying
m = 0.1666666667n

Subproblem 2
Set the factor '(7m + 11n)' equal to zero and attempt to solve:

Simplifying
7m + 11n = 0

Solving
7m + 11n = 0

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

Add '-11n' to each side of the equation.
7m + 11n + -11n = 0 + -11n

Combine like terms: 11n + -11n = 0
7m + 0 = 0 + -11n
7m = 0 + -11n
Remove the zero:
7m = -11n

Divide each side by '7'.
m = -1.571428571n

Simplifying
m = -1.571428571n
Solution
m = {0.1666666667n, -1.571428571n}

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