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

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

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

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

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

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

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

Solving
-1mn + m2 + -6n2 = 0

Solving for variable 'm'.

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

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

Simplifying
m + 2n = 0

Solving
m + 2n = 0

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

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

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

Simplifying
m = -2n
Solution
m = {3n, -2n}