(-7m+5n)*(3m+n)=

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Solution for (-7m+5n)*(3m+n)= equation: 


Simplifying
(-7m + 5n)(3m + n) = 0

Multiply (-7m + 5n) * (3m + n)
(-7m * (3m + n) + 5n * (3m + n)) = 0
((3m * -7m + n * -7m) + 5n * (3m + n)) = 0

Reorder the terms:
((-7mn + -21m2) + 5n * (3m + n)) = 0
((-7mn + -21m2) + 5n * (3m + n)) = 0
(-7mn + -21m2 + (3m * 5n + n * 5n)) = 0
(-7mn + -21m2 + (15mn + 5n2)) = 0

Reorder the terms:
(-7mn + 15mn + -21m2 + 5n2) = 0

Combine like terms: -7mn + 15mn = 8mn
(8mn + -21m2 + 5n2) = 0

Solving
8mn + -21m2 + 5n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-3m + -1n)(7m + -5n) = 0


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

Simplifying
-3m + -1n = 0

Solving
-3m + -1n = 0

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

Add 'n' to each side of the equation.
-3m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
-3m + 0 = 0 + n
-3m = 0 + n
Remove the zero:
-3m = n

Divide each side by '-3'.
m = -0.3333333333n

Simplifying
m = -0.3333333333n

Subproblem 2
Set the factor '(7m + -5n)' equal to zero and attempt to solve:

Simplifying
7m + -5n = 0

Solving
7m + -5n = 0

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

Add '5n' to each side of the equation.
7m + -5n + 5n = 0 + 5n

Combine like terms: -5n + 5n = 0
7m + 0 = 0 + 5n
7m = 0 + 5n
Remove the zero:
7m = 5n

Divide each side by '7'.
m = 0.7142857143n

Simplifying
m = 0.7142857143n
Solution
m = {-0.3333333333n, 0.7142857143n}

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