(m+5n)(m-3n)=

Solution for (m+5n)(m-3n)= equation:

Simplifying
(m + 5n)(m + -3n) = 0

Multiply (m + 5n) * (m + -3n)
(m(m + -3n) + 5n * (m + -3n)) = 0
((m * m + -3n * m) + 5n * (m + -3n)) = 0

Reorder the terms:
((-3mn + m2) + 5n * (m + -3n)) = 0
((-3mn + m2) + 5n * (m + -3n)) = 0
(-3mn + m2 + (m * 5n + -3n * 5n)) = 0
(-3mn + m2 + (5mn + -15n2)) = 0

Reorder the terms:
(-3mn + 5mn + m2 + -15n2) = 0

Combine like terms: -3mn + 5mn = 2mn
(2mn + m2 + -15n2) = 0

Solving
2mn + m2 + -15n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -3n)(m + 5n) = 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 + 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 = {3n, -5n}