6m^2-36-162n^2=0

Solution for 6m^2-36-162n^2=0 equation:

Simplifying
6m2 + -36 + -162n2 = 0

Reorder the terms:
-36 + 6m2 + -162n2 = 0

Solving
-36 + 6m2 + -162n2 = 0

Solving for variable 'm'.

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

Add '36' to each side of the equation.
-36 + 6m2 + 36 + -162n2 = 0 + 36

Reorder the terms:
-36 + 36 + 6m2 + -162n2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 6m2 + -162n2 = 0 + 36
6m2 + -162n2 = 0 + 36

Combine like terms: 0 + 36 = 36
6m2 + -162n2 = 36

Add '162n2' to each side of the equation.
6m2 + -162n2 + 162n2 = 36 + 162n2

Combine like terms: -162n2 + 162n2 = 0
6m2 + 0 = 36 + 162n2
6m2 = 36 + 162n2

Divide each side by '6'.
m2 = 6 + 27n2

Simplifying
m2 = 6 + 27n2

Reorder the terms:
-6 + m2 + -27n2 = 6 + 27n2 + -6 + -27n2

Reorder the terms:
-6 + m2 + -27n2 = 6 + -6 + 27n2 + -27n2

Combine like terms: 6 + -6 = 0
-6 + m2 + -27n2 = 0 + 27n2 + -27n2
-6 + m2 + -27n2 = 27n2 + -27n2

Combine like terms: 27n2 + -27n2 = 0
-6 + m2 + -27n2 = 0

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

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 + 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
Solution
m = {9n, -3n}