(9m-3n)(5m+6n)=

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Solution for (9m-3n)(5m+6n)= equation: 


Simplifying
(9m + -3n)(5m + 6n) = 0

Multiply (9m + -3n) * (5m + 6n)
(9m * (5m + 6n) + -3n * (5m + 6n)) = 0
((5m * 9m + 6n * 9m) + -3n * (5m + 6n)) = 0

Reorder the terms:
((54mn + 45m2) + -3n * (5m + 6n)) = 0
((54mn + 45m2) + -3n * (5m + 6n)) = 0
(54mn + 45m2 + (5m * -3n + 6n * -3n)) = 0
(54mn + 45m2 + (-15mn + -18n2)) = 0

Reorder the terms:
(54mn + -15mn + 45m2 + -18n2) = 0

Combine like terms: 54mn + -15mn = 39mn
(39mn + 45m2 + -18n2) = 0

Solving
39mn + 45m2 + -18n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(13mn + 15m2 + -6n2) = 0

Factor a trinomial.
3((3m + -1n)(5m + 6n)) = 0

Ignore the factor 3.

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

Simplifying
3m + -1n = 0

Solving
3m + -1n = 0

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

Add 'n' to each side of the equation.
3m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
3m + 0 = 0 + n
3m = 0 + n
Remove the zero:
3m = n

Divide each side by '3'.
m = 0.3333333333n

Simplifying
m = 0.3333333333n

Subproblem 2
Set the factor '(5m + 6n)' equal to zero and attempt to solve:

Simplifying
5m + 6n = 0

Solving
5m + 6n = 0

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

Add '-6n' to each side of the equation.
5m + 6n + -6n = 0 + -6n

Combine like terms: 6n + -6n = 0
5m + 0 = 0 + -6n
5m = 0 + -6n
Remove the zero:
5m = -6n

Divide each side by '5'.
m = -1.2n

Simplifying
m = -1.2n
Solution
m = {0.3333333333n, -1.2n}

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