(3m-2n)(3m+5n)=

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Solution for (3m-2n)(3m+5n)= equation: 


Simplifying
(3m + -2n)(3m + 5n) = 0

Multiply (3m + -2n) * (3m + 5n)
(3m * (3m + 5n) + -2n * (3m + 5n)) = 0
((3m * 3m + 5n * 3m) + -2n * (3m + 5n)) = 0

Reorder the terms:
((15mn + 9m2) + -2n * (3m + 5n)) = 0
((15mn + 9m2) + -2n * (3m + 5n)) = 0
(15mn + 9m2 + (3m * -2n + 5n * -2n)) = 0
(15mn + 9m2 + (-6mn + -10n2)) = 0

Reorder the terms:
(15mn + -6mn + 9m2 + -10n2) = 0

Combine like terms: 15mn + -6mn = 9mn
(9mn + 9m2 + -10n2) = 0

Solving
9mn + 9m2 + -10n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(3m + -2n)(3m + 5n) = 0


Subproblem 1
Set the factor '(3m + -2n)' equal to zero and attempt to solve:

Simplifying
3m + -2n = 0

Solving
3m + -2n = 0

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

Add '2n' to each side of the equation.
3m + -2n + 2n = 0 + 2n

Combine like terms: -2n + 2n = 0
3m + 0 = 0 + 2n
3m = 0 + 2n
Remove the zero:
3m = 2n

Divide each side by '3'.
m = 0.6666666667n

Simplifying
m = 0.6666666667n

Subproblem 2
Set the factor '(3m + 5n)' equal to zero and attempt to solve:

Simplifying
3m + 5n = 0

Solving
3m + 5n = 0

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

Add '-5n' to each side of the equation.
3m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
3m + 0 = 0 + -5n
3m = 0 + -5n
Remove the zero:
3m = -5n

Divide each side by '3'.
m = -1.666666667n

Simplifying
m = -1.666666667n
Solution
m = {0.6666666667n, -1.666666667n}

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