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

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


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

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

Reorder the terms:
((-16mn + 20m2) + 3n * (5m + -4n)) = 0
((-16mn + 20m2) + 3n * (5m + -4n)) = 0
(-16mn + 20m2 + (5m * 3n + -4n * 3n)) = 0
(-16mn + 20m2 + (15mn + -12n2)) = 0

Reorder the terms:
(-16mn + 15mn + 20m2 + -12n2) = 0

Combine like terms: -16mn + 15mn = -1mn
(-1mn + 20m2 + -12n2) = 0

Solving
-1mn + 20m2 + -12n2 = 0

Solving for variable 'm'.

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


Subproblem 1
Set the factor '(5m + -4n)' equal to zero and attempt to solve:

Simplifying
5m + -4n = 0

Solving
5m + -4n = 0

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

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

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

Divide each side by '5'.
m = 0.8n

Simplifying
m = 0.8n

Subproblem 2
Set the factor '(4m + 3n)' equal to zero and attempt to solve:

Simplifying
4m + 3n = 0

Solving
4m + 3n = 0

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

Add '-3n' to each side of the equation.
4m + 3n + -3n = 0 + -3n

Combine like terms: 3n + -3n = 0
4m + 0 = 0 + -3n
4m = 0 + -3n
Remove the zero:
4m = -3n

Divide each side by '4'.
m = -0.75n

Simplifying
m = -0.75n
Solution
m = {0.8n, -0.75n}

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