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

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


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

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

Reorder the terms:
((-12mn + 20m2) + 5n * (5m + -3n)) = 0
((-12mn + 20m2) + 5n * (5m + -3n)) = 0
(-12mn + 20m2 + (5m * 5n + -3n * 5n)) = 0
(-12mn + 20m2 + (25mn + -15n2)) = 0

Reorder the terms:
(-12mn + 25mn + 20m2 + -15n2) = 0

Combine like terms: -12mn + 25mn = 13mn
(13mn + 20m2 + -15n2) = 0

Solving
13mn + 20m2 + -15n2 = 0

Solving for variable 'm'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(4m + 5n)' equal to zero and attempt to solve:

Simplifying
4m + 5n = 0

Solving
4m + 5n = 0

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

Add '-5n' to each side of the equation.
4m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
4m + 0 = 0 + -5n
4m = 0 + -5n
Remove the zero:
4m = -5n

Divide each side by '4'.
m = -1.25n

Simplifying
m = -1.25n
Solution
m = {0.6n, -1.25n}

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