(9m-2n)(3m+10n)=

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Solution for (9m-2n)(3m+10n)= equation: 


Simplifying
(9m + -2n)(3m + 10n) = 0

Multiply (9m + -2n) * (3m + 10n)
(9m * (3m + 10n) + -2n * (3m + 10n)) = 0
((3m * 9m + 10n * 9m) + -2n * (3m + 10n)) = 0

Reorder the terms:
((90mn + 27m2) + -2n * (3m + 10n)) = 0
((90mn + 27m2) + -2n * (3m + 10n)) = 0
(90mn + 27m2 + (3m * -2n + 10n * -2n)) = 0
(90mn + 27m2 + (-6mn + -20n2)) = 0

Reorder the terms:
(90mn + -6mn + 27m2 + -20n2) = 0

Combine like terms: 90mn + -6mn = 84mn
(84mn + 27m2 + -20n2) = 0

Solving
84mn + 27m2 + -20n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(9m + -2n)(3m + 10n) = 0


Subproblem 1
Set the factor '(9m + -2n)' equal to zero and attempt to solve:

Simplifying
9m + -2n = 0

Solving
9m + -2n = 0

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

Add '2n' to each side of the equation.
9m + -2n + 2n = 0 + 2n

Combine like terms: -2n + 2n = 0
9m + 0 = 0 + 2n
9m = 0 + 2n
Remove the zero:
9m = 2n

Divide each side by '9'.
m = 0.2222222222n

Simplifying
m = 0.2222222222n

Subproblem 2
Set the factor '(3m + 10n)' equal to zero and attempt to solve:

Simplifying
3m + 10n = 0

Solving
3m + 10n = 0

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

Add '-10n' to each side of the equation.
3m + 10n + -10n = 0 + -10n

Combine like terms: 10n + -10n = 0
3m + 0 = 0 + -10n
3m = 0 + -10n
Remove the zero:
3m = -10n

Divide each side by '3'.
m = -3.333333333n

Simplifying
m = -3.333333333n
Solution
m = {0.2222222222n, -3.333333333n}

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