(11m-3n)(4m+12n)=

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Solution for (11m-3n)(4m+12n)= equation: 


Simplifying
(11m + -3n)(4m + 12n) = 0

Multiply (11m + -3n) * (4m + 12n)
(11m * (4m + 12n) + -3n * (4m + 12n)) = 0
((4m * 11m + 12n * 11m) + -3n * (4m + 12n)) = 0

Reorder the terms:
((132mn + 44m2) + -3n * (4m + 12n)) = 0
((132mn + 44m2) + -3n * (4m + 12n)) = 0
(132mn + 44m2 + (4m * -3n + 12n * -3n)) = 0
(132mn + 44m2 + (-12mn + -36n2)) = 0

Reorder the terms:
(132mn + -12mn + 44m2 + -36n2) = 0

Combine like terms: 132mn + -12mn = 120mn
(120mn + 44m2 + -36n2) = 0

Solving
120mn + 44m2 + -36n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(30mn + 11m2 + -9n2) = 0

Factor a trinomial.
4((11m + -3n)(m + 3n)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(11m + -3n)' equal to zero and attempt to solve:

Simplifying
11m + -3n = 0

Solving
11m + -3n = 0

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

Add '3n' to each side of the equation.
11m + -3n + 3n = 0 + 3n

Combine like terms: -3n + 3n = 0
11m + 0 = 0 + 3n
11m = 0 + 3n
Remove the zero:
11m = 3n

Divide each side by '11'.
m = 0.2727272727n

Simplifying
m = 0.2727272727n

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

Simplifying
m + 3n = 0

Solving
m + 3n = 0

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

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

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

Simplifying
m = -3n
Solution
m = {0.2727272727n, -3n}

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