m(m+7n)+3n(m+7n)=

Solution for m(m+7n)+3n(m+7n)= equation:

Simplifying
m(m + 7n) + 3n(m + 7n) = 0
(m * m + 7n * m) + 3n(m + 7n) = 0

Reorder the terms:
(7mn + m2) + 3n(m + 7n) = 0
(7mn + m2) + 3n(m + 7n) = 0
7mn + m2 + (m * 3n + 7n * 3n) = 0
7mn + m2 + (3mn + 21n2) = 0

Reorder the terms:
7mn + 3mn + m2 + 21n2 = 0

Combine like terms: 7mn + 3mn = 10mn
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}