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

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

Simplifying
(m + 3n)(2m + -1n) = 0

Multiply (m + 3n) * (2m + -1n)
(m(2m + -1n) + 3n * (2m + -1n)) = 0
((2m * m + -1n * m) + 3n * (2m + -1n)) = 0

Reorder the terms:
((-1mn + 2m2) + 3n * (2m + -1n)) = 0
((-1mn + 2m2) + 3n * (2m + -1n)) = 0
(-1mn + 2m2 + (2m * 3n + -1n * 3n)) = 0
(-1mn + 2m2 + (6mn + -3n2)) = 0

Reorder the terms:
(-1mn + 6mn + 2m2 + -3n2) = 0

Combine like terms: -1mn + 6mn = 5mn
(5mn + 2m2 + -3n2) = 0

Solving
5mn + 2m2 + -3n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2m + -1n)(m + 3n) = 0

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

Simplifying
2m + -1n = 0

Solving
2m + -1n = 0

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

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

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

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

Simplifying
m = 0.5n
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 = {0.5n, -3n}