m(m+2n)+5n(m+2n)=

Solution for m(m+2n)+5n(m+2n)= equation:

Simplifying
m(m + 2n) + 5n(m + 2n) = 0
(m * m + 2n * m) + 5n(m + 2n) = 0

Reorder the terms:
(2mn + m2) + 5n(m + 2n) = 0
(2mn + m2) + 5n(m + 2n) = 0
2mn + m2 + (m * 5n + 2n * 5n) = 0
2mn + m2 + (5mn + 10n2) = 0

Reorder the terms:
2mn + 5mn + m2 + 10n2 = 0

Combine like terms: 2mn + 5mn = 7mn
7mn + m2 + 10n2 = 0

Solving
7mn + m2 + 10n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + 2n)(m + 5n) = 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 + 5n)' equal to zero and attempt to solve:

Simplifying
m + 5n = 0

Solving
m + 5n = 0

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

Add '-5n' to each side of the equation.
m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
m + 0 = 0 + -5n
m = 0 + -5n
Remove the zero:
m = -5n

Simplifying
m = -5n
Solution
m = {-2n, -5n}