m^2+23mn+42n^2=0

Solution for m^2+23mn+42n^2=0 equation:

Simplifying
m2 + 23mn + 42n2 = 0

Reorder the terms:
23mn + m2 + 42n2 = 0

Solving
23mn + m2 + 42n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + 2n)(m + 21n) = 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 + 21n)' equal to zero and attempt to solve:

Simplifying
m + 21n = 0

Solving
m + 21n = 0

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

Add '-21n' to each side of the equation.
m + 21n + -21n = 0 + -21n

Combine like terms: 21n + -21n = 0
m + 0 = 0 + -21n
m = 0 + -21n
Remove the zero:
m = -21n

Simplifying
m = -21n
Solution
m = {-2n, -21n}