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

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Solution for (m+3n)(6m-5n)=0 equation: 


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

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

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

Reorder the terms:
(-5mn + 18mn + 6m2 + -15n2) = 0

Combine like terms: -5mn + 18mn = 13mn
(13mn + 6m2 + -15n2) = 0

Solving
13mn + 6m2 + -15n2 = 0

Solving for variable 'm'.

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


Subproblem 1
Set the factor '(6m + -5n)' equal to zero and attempt to solve:

Simplifying
6m + -5n = 0

Solving
6m + -5n = 0

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

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

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

Divide each side by '6'.
m = 0.8333333333n

Simplifying
m = 0.8333333333n

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

Simplifying
m + 3n = 0

Solving
m + 3n = 0

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

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

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

Simplifying
m = -3n
Solution
m = {0.8333333333n, -3n}

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