(3m-6n)(m+4n)=0

Solution for (3m-6n)(m+4n)=0 equation:

Simplifying
(3m + -6n)(m + 4n) = 0

Multiply (3m + -6n) * (m + 4n)
(3m * (m + 4n) + -6n * (m + 4n)) = 0
((m * 3m + 4n * 3m) + -6n * (m + 4n)) = 0

Reorder the terms:
((12mn + 3m2) + -6n * (m + 4n)) = 0
((12mn + 3m2) + -6n * (m + 4n)) = 0
(12mn + 3m2 + (m * -6n + 4n * -6n)) = 0
(12mn + 3m2 + (-6mn + -24n2)) = 0

Reorder the terms:
(12mn + -6mn + 3m2 + -24n2) = 0

Combine like terms: 12mn + -6mn = 6mn
(6mn + 3m2 + -24n2) = 0

Solving
6mn + 3m2 + -24n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2mn + m2 + -8n2) = 0

Factor a trinomial.
3((m + -2n)(m + 4n)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(m + 4n)' equal to zero and attempt to solve:

Simplifying
m + 4n = 0

Solving
m + 4n = 0

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

Add '-4n' to each side of the equation.
m + 4n + -4n = 0 + -4n

Combine like terms: 4n + -4n = 0
m + 0 = 0 + -4n
m = 0 + -4n
Remove the zero:
m = -4n

Simplifying
m = -4n
Solution
m = {2n, -4n}