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

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


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

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

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

Reorder the terms:
(3mn + 10mn + 6m2 + 5n2) = 0

Combine like terms: 3mn + 10mn = 13mn
(13mn + 6m2 + 5n2) = 0

Solving
13mn + 6m2 + 5n2 = 0

Solving for variable 'm'.

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


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

Simplifying
2m + n = 0

Solving
2m + n = 0

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

Add '-1n' to each side of the equation.
2m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
2m + 0 = 0 + -1n
2m = 0 + -1n
Remove the zero:
2m = -1n

Divide each side by '2'.
m = -0.5n

Simplifying
m = -0.5n

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 = {-0.5n, -1.666666667n}

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