m(m+6n)+7n(m+6n)=

Solution for m(m+6n)+7n(m+6n)= equation:

Simplifying
m(m + 6n) + 7n(m + 6n) = 0
(m * m + 6n * m) + 7n(m + 6n) = 0

Reorder the terms:
(6mn + m2) + 7n(m + 6n) = 0
(6mn + m2) + 7n(m + 6n) = 0
6mn + m2 + (m * 7n + 6n * 7n) = 0
6mn + m2 + (7mn + 42n2) = 0

Reorder the terms:
6mn + 7mn + m2 + 42n2 = 0

Combine like terms: 6mn + 7mn = 13mn
13mn + m2 + 42n2 = 0

Solving
13mn + m2 + 42n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + 6n)(m + 7n) = 0

Subproblem 1
Set the factor '(m + 6n)' equal to zero and attempt to solve:

Simplifying
m + 6n = 0

Solving
m + 6n = 0

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

Add '-6n' to each side of the equation.
m + 6n + -6n = 0 + -6n

Combine like terms: 6n + -6n = 0
m + 0 = 0 + -6n
m = 0 + -6n
Remove the zero:
m = -6n

Simplifying
m = -6n
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 = {-6n, -7n}