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

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

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

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

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

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

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

Solving
-1mn + 2m2 + -3n2 = 0

Solving for variable 'm'.

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

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

Simplifying
2m + -3n = 0

Solving
2m + -3n = 0

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

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

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

Divide each side by '2'.
m = 1.5n

Simplifying
m = 1.5n
Subproblem 2
Set the factor '(m + n)' equal to zero and attempt to solve:

Simplifying
m + n = 0

Solving
m + n = 0

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

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

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

Simplifying
m = -1n
Solution
m = {1.5n, -1n}