(7m+5n)(5m-7n)=

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Solution for (7m+5n)(5m-7n)= equation: 


Simplifying
(7m + 5n)(5m + -7n) = 0

Multiply (7m + 5n) * (5m + -7n)
(7m * (5m + -7n) + 5n * (5m + -7n)) = 0
((5m * 7m + -7n * 7m) + 5n * (5m + -7n)) = 0

Reorder the terms:
((-49mn + 35m2) + 5n * (5m + -7n)) = 0
((-49mn + 35m2) + 5n * (5m + -7n)) = 0
(-49mn + 35m2 + (5m * 5n + -7n * 5n)) = 0
(-49mn + 35m2 + (25mn + -35n2)) = 0

Reorder the terms:
(-49mn + 25mn + 35m2 + -35n2) = 0

Combine like terms: -49mn + 25mn = -24mn
(-24mn + 35m2 + -35n2) = 0

Solving
-24mn + 35m2 + -35n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(5m + -7n)(7m + 5n) = 0


Subproblem 1
Set the factor '(5m + -7n)' equal to zero and attempt to solve:

Simplifying
5m + -7n = 0

Solving
5m + -7n = 0

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

Add '7n' to each side of the equation.
5m + -7n + 7n = 0 + 7n

Combine like terms: -7n + 7n = 0
5m + 0 = 0 + 7n
5m = 0 + 7n
Remove the zero:
5m = 7n

Divide each side by '5'.
m = 1.4n

Simplifying
m = 1.4n

Subproblem 2
Set the factor '(7m + 5n)' equal to zero and attempt to solve:

Simplifying
7m + 5n = 0

Solving
7m + 5n = 0

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

Add '-5n' to each side of the equation.
7m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
7m + 0 = 0 + -5n
7m = 0 + -5n
Remove the zero:
7m = -5n

Divide each side by '7'.
m = -0.7142857143n

Simplifying
m = -0.7142857143n
Solution
m = {1.4n, -0.7142857143n}

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