3m^2-21mn-54n^2=0

Solution for 3m^2-21mn-54n^2=0 equation:

Simplifying
3m2 + -21mn + -54n2 = 0

Reorder the terms:
-21mn + 3m2 + -54n2 = 0

Solving
-21mn + 3m2 + -54n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7mn + m2 + -18n2) = 0

Factor a trinomial.
3((m + -9n)(m + 2n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(m + -9n)' equal to zero and attempt to solve:

Simplifying
m + -9n = 0

Solving
m + -9n = 0

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

Add '9n' to each side of the equation.
m + -9n + 9n = 0 + 9n

Combine like terms: -9n + 9n = 0
m + 0 = 0 + 9n
m = 0 + 9n
Remove the zero:
m = 9n

Simplifying
m = 9n
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 = {9n, -2n}