(9m-4n)(3m+12n)=

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Solution for (9m-4n)(3m+12n)= equation: 


Simplifying
(9m + -4n)(3m + 12n) = 0

Multiply (9m + -4n) * (3m + 12n)
(9m * (3m + 12n) + -4n * (3m + 12n)) = 0
((3m * 9m + 12n * 9m) + -4n * (3m + 12n)) = 0

Reorder the terms:
((108mn + 27m2) + -4n * (3m + 12n)) = 0
((108mn + 27m2) + -4n * (3m + 12n)) = 0
(108mn + 27m2 + (3m * -4n + 12n * -4n)) = 0
(108mn + 27m2 + (-12mn + -48n2)) = 0

Reorder the terms:
(108mn + -12mn + 27m2 + -48n2) = 0

Combine like terms: 108mn + -12mn = 96mn
(96mn + 27m2 + -48n2) = 0

Solving
96mn + 27m2 + -48n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(32mn + 9m2 + -16n2) = 0

Factor a trinomial.
3((9m + -4n)(m + 4n)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9m + -4n)' equal to zero and attempt to solve:

Simplifying
9m + -4n = 0

Solving
9m + -4n = 0

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

Add '4n' to each side of the equation.
9m + -4n + 4n = 0 + 4n

Combine like terms: -4n + 4n = 0
9m + 0 = 0 + 4n
9m = 0 + 4n
Remove the zero:
9m = 4n

Divide each side by '9'.
m = 0.4444444444n

Simplifying
m = 0.4444444444n

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

Simplifying
m + 4n = 0

Solving
m + 4n = 0

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

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

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

Simplifying
m = -4n
Solution
m = {0.4444444444n, -4n}

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