m(m+2n)+n(m+2n)=

Solution for m(m+2n)+n(m+2n)= equation:

Simplifying
m(m + 2n) + n(m + 2n) = 0
(m * m + 2n * m) + n(m + 2n) = 0

Reorder the terms:
(2mn + m2) + n(m + 2n) = 0
(2mn + m2) + n(m + 2n) = 0
2mn + m2 + (m * n + 2n * n) = 0
2mn + m2 + (mn + 2n2) = 0

Reorder the terms:
2mn + mn + m2 + 2n2 = 0

Combine like terms: 2mn + mn = 3mn
3mn + m2 + 2n2 = 0

Solving
3mn + m2 + 2n2 = 0

Solving for variable 'm'.

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

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

Simplifying
m + n = 0

Solving
m + n = 0

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

Add '-1n' to each side of the equation.
m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
m + 0 = 0 + -1n
m = 0 + -1n
Remove the zero:
m = -1n

Simplifying
m = -1n
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 = {-1n, -2n}