m^2-mn-42n^2=0

Solution for m^2-mn-42n^2=0 equation:

Simplifying
m2 + -1mn + -42n2 = 0

Reorder the terms:
-1mn + m2 + -42n2 = 0

Solving
-1mn + m2 + -42n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -7n)(m + 6n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(m + 6n)' equal to zero and attempt to solve:

Simplifying
m + 6n = 0

Solving
m + 6n = 0

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

Add '-6n' to each side of the equation.
m + 6n + -6n = 0 + -6n

Combine like terms: 6n + -6n = 0
m + 0 = 0 + -6n
m = 0 + -6n
Remove the zero:
m = -6n

Simplifying
m = -6n
Solution
m = {7n, -6n}