5m(3m-2n)-6n(-2n+3m)=

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Solution for 5m(3m-2n)-6n(-2n+3m)= equation: 


Simplifying
5m(3m + -2n) + -6n(-2n + 3m) = 0
(3m * 5m + -2n * 5m) + -6n(-2n + 3m) = 0

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

Reorder the terms:
-10mn + 15m2 + -6n(3m + -2n) = 0
-10mn + 15m2 + (3m * -6n + -2n * -6n) = 0
-10mn + 15m2 + (-18mn + 12n2) = 0

Reorder the terms:
-10mn + -18mn + 15m2 + 12n2 = 0

Combine like terms: -10mn + -18mn = -28mn
-28mn + 15m2 + 12n2 = 0

Solving
-28mn + 15m2 + 12n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(5m + -6n)(3m + -2n) = 0


Subproblem 1
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

Subproblem 2
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
Solution
m = {1.2n, 0.6666666667n}

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