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

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


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

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

Reorder the terms:
((-9mn + 12m2) + 4n * (4m + -3n)) = 0
((-9mn + 12m2) + 4n * (4m + -3n)) = 0
(-9mn + 12m2 + (4m * 4n + -3n * 4n)) = 0
(-9mn + 12m2 + (16mn + -12n2)) = 0

Reorder the terms:
(-9mn + 16mn + 12m2 + -12n2) = 0

Combine like terms: -9mn + 16mn = 7mn
(7mn + 12m2 + -12n2) = 0

Solving
7mn + 12m2 + -12n2 = 0

Solving for variable 'm'.

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


Subproblem 1
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

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

Simplifying
3m + 4n = 0

Solving
3m + 4n = 0

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

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

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

Divide each side by '3'.
m = -1.333333333n

Simplifying
m = -1.333333333n
Solution
m = {0.75n, -1.333333333n}

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