m(m+8n)+7n(m+8n)=0

Solution for m(m+8n)+7n(m+8n)=0 equation:

Simplifying
m(m + 8n) + 7n(m + 8n) = 0
(m * m + 8n * m) + 7n(m + 8n) = 0

Reorder the terms:
(8mn + m2) + 7n(m + 8n) = 0
(8mn + m2) + 7n(m + 8n) = 0
8mn + m2 + (m * 7n + 8n * 7n) = 0
8mn + m2 + (7mn + 56n2) = 0

Reorder the terms:
8mn + 7mn + m2 + 56n2 = 0

Combine like terms: 8mn + 7mn = 15mn
15mn + m2 + 56n2 = 0

Solving
15mn + m2 + 56n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + 7n)(m + 8n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(m + 8n)' equal to zero and attempt to solve:

Simplifying
m + 8n = 0

Solving
m + 8n = 0

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

Add '-8n' to each side of the equation.
m + 8n + -8n = 0 + -8n

Combine like terms: 8n + -8n = 0
m + 0 = 0 + -8n
m = 0 + -8n
Remove the zero:
m = -8n

Simplifying
m = -8n
Solution
m = {-7n, -8n}