(4m-7n)(9m+3n)=

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Solution for (4m-7n)(9m+3n)= equation: 


Simplifying
(4m + -7n)(9m + 3n) = 0

Multiply (4m + -7n) * (9m + 3n)
(4m * (9m + 3n) + -7n * (9m + 3n)) = 0
((9m * 4m + 3n * 4m) + -7n * (9m + 3n)) = 0

Reorder the terms:
((12mn + 36m2) + -7n * (9m + 3n)) = 0
((12mn + 36m2) + -7n * (9m + 3n)) = 0
(12mn + 36m2 + (9m * -7n + 3n * -7n)) = 0
(12mn + 36m2 + (-63mn + -21n2)) = 0

Reorder the terms:
(12mn + -63mn + 36m2 + -21n2) = 0

Combine like terms: 12mn + -63mn = -51mn
(-51mn + 36m2 + -21n2) = 0

Solving
-51mn + 36m2 + -21n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-17mn + 12m2 + -7n2) = 0

Factor a trinomial.
3((4m + -7n)(3m + n)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4m + -7n)' equal to zero and attempt to solve:

Simplifying
4m + -7n = 0

Solving
4m + -7n = 0

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

Add '7n' to each side of the equation.
4m + -7n + 7n = 0 + 7n

Combine like terms: -7n + 7n = 0
4m + 0 = 0 + 7n
4m = 0 + 7n
Remove the zero:
4m = 7n

Divide each side by '4'.
m = 1.75n

Simplifying
m = 1.75n

Subproblem 2
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
Solution
m = {1.75n, -0.3333333333n}

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