6m^2+60mn+96n^2=0

Solution for 6m^2+60mn+96n^2=0 equation:

Simplifying
6m2 + 60mn + 96n2 = 0

Reorder the terms:
60mn + 6m2 + 96n2 = 0

Solving
60mn + 6m2 + 96n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '6'.
6(10mn + m2 + 16n2) = 0

Factor a trinomial.
6((m + 2n)(m + 8n)) = 0

Ignore the factor 6.
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 + 8n)' equal to zero and attempt to solve:

Simplifying
m + 8n = 0

Solving
m + 8n = 0

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

Add '-8n' to each side of the equation.
m + 8n + -8n = 0 + -8n

Combine like terms: 8n + -8n = 0
m + 0 = 0 + -8n
m = 0 + -8n
Remove the zero:
m = -8n

Simplifying
m = -8n
Solution
m = {-2n, -8n}