m^2+5mn-14n^2=0

Solution for m^2+5mn-14n^2=0 equation:

Simplifying
m2 + 5mn + -14n2 = 0

Reorder the terms:
5mn + m2 + -14n2 = 0

Solving
5mn + m2 + -14n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -2n)(m + 7n) = 0

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 + 7n)' equal to zero and attempt to solve:

Simplifying
m + 7n = 0

Solving
m + 7n = 0

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

Add '-7n' to each side of the equation.
m + 7n + -7n = 0 + -7n

Combine like terms: 7n + -7n = 0
m + 0 = 0 + -7n
m = 0 + -7n
Remove the zero:
m = -7n

Simplifying
m = -7n
Solution
m = {2n, -7n}