m^2-14mn-32n^2=0

Solution for m^2-14mn-32n^2=0 equation:

Simplifying
m2 + -14mn + -32n2 = 0

Reorder the terms:
-14mn + m2 + -32n2 = 0

Solving
-14mn + m2 + -32n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -16n)(m + 2n) = 0

Subproblem 1
Set the factor '(m + -16n)' equal to zero and attempt to solve:

Simplifying
m + -16n = 0

Solving
m + -16n = 0

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

Add '16n' to each side of the equation.
m + -16n + 16n = 0 + 16n

Combine like terms: -16n + 16n = 0
m + 0 = 0 + 16n
m = 0 + 16n
Remove the zero:
m = 16n

Simplifying
m = 16n
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 = {16n, -2n}