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

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


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

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

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

Reorder the terms:
(mn + -21mn + 7m2 + -3n2) = 0

Combine like terms: mn + -21mn = -20mn
(-20mn + 7m2 + -3n2) = 0

Solving
-20mn + 7m2 + -3n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -3n)(7m + n) = 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 '(7m + n)' equal to zero and attempt to solve:

Simplifying
7m + n = 0

Solving
7m + n = 0

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

Add '-1n' to each side of the equation.
7m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
7m + 0 = 0 + -1n
7m = 0 + -1n
Remove the zero:
7m = -1n

Divide each side by '7'.
m = -0.1428571429n

Simplifying
m = -0.1428571429n
Solution
m = {3n, -0.1428571429n}

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