(2m-3n)(m+5n)=

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Solution for (2m-3n)(m+5n)= equation: 


Simplifying
(2m + -3n)(m + 5n) = 0

Multiply (2m + -3n) * (m + 5n)
(2m * (m + 5n) + -3n * (m + 5n)) = 0
((m * 2m + 5n * 2m) + -3n * (m + 5n)) = 0

Reorder the terms:
((10mn + 2m2) + -3n * (m + 5n)) = 0
((10mn + 2m2) + -3n * (m + 5n)) = 0
(10mn + 2m2 + (m * -3n + 5n * -3n)) = 0
(10mn + 2m2 + (-3mn + -15n2)) = 0

Reorder the terms:
(10mn + -3mn + 2m2 + -15n2) = 0

Combine like terms: 10mn + -3mn = 7mn
(7mn + 2m2 + -15n2) = 0

Solving
7mn + 2m2 + -15n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2m + -3n)(m + 5n) = 0


Subproblem 1
Set the factor '(2m + -3n)' equal to zero and attempt to solve:

Simplifying
2m + -3n = 0

Solving
2m + -3n = 0

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

Add '3n' to each side of the equation.
2m + -3n + 3n = 0 + 3n

Combine like terms: -3n + 3n = 0
2m + 0 = 0 + 3n
2m = 0 + 3n
Remove the zero:
2m = 3n

Divide each side by '2'.
m = 1.5n

Simplifying
m = 1.5n

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 = {1.5n, -5n}

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