(5m+3n)(4m-n)=

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Solution for (5m+3n)(4m-n)= equation: 


Simplifying
(5m + 3n)(4m + -1n) = 0

Multiply (5m + 3n) * (4m + -1n)
(5m * (4m + -1n) + 3n * (4m + -1n)) = 0
((4m * 5m + -1n * 5m) + 3n * (4m + -1n)) = 0

Reorder the terms:
((-5mn + 20m2) + 3n * (4m + -1n)) = 0
((-5mn + 20m2) + 3n * (4m + -1n)) = 0
(-5mn + 20m2 + (4m * 3n + -1n * 3n)) = 0
(-5mn + 20m2 + (12mn + -3n2)) = 0

Reorder the terms:
(-5mn + 12mn + 20m2 + -3n2) = 0

Combine like terms: -5mn + 12mn = 7mn
(7mn + 20m2 + -3n2) = 0

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

Solving for variable 'm'.

Factor a trinomial.
(4m + -1n)(5m + 3n) = 0


Subproblem 1
Set the factor '(4m + -1n)' equal to zero and attempt to solve:

Simplifying
4m + -1n = 0

Solving
4m + -1n = 0

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

Add 'n' to each side of the equation.
4m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
4m + 0 = 0 + n
4m = 0 + n
Remove the zero:
4m = n

Divide each side by '4'.
m = 0.25n

Simplifying
m = 0.25n

Subproblem 2
Set the factor '(5m + 3n)' equal to zero and attempt to solve:

Simplifying
5m + 3n = 0

Solving
5m + 3n = 0

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

Add '-3n' to each side of the equation.
5m + 3n + -3n = 0 + -3n

Combine like terms: 3n + -3n = 0
5m + 0 = 0 + -3n
5m = 0 + -3n
Remove the zero:
5m = -3n

Divide each side by '5'.
m = -0.6n

Simplifying
m = -0.6n
Solution
m = {0.25n, -0.6n}

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