m^2+10mn+21n^2=0

Solution for m^2+10mn+21n^2=0 equation:

Simplifying
m2 + 10mn + 21n2 = 0

Reorder the terms:
10mn + m2 + 21n2 = 0

Solving
10mn + m2 + 21n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + 3n)(m + 7n) = 0

Subproblem 1
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
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 = {-3n, -7n}