(7m-5n)(2m+5n)=

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Solution for (7m-5n)(2m+5n)= equation: 


Simplifying
(7m + -5n)(2m + 5n) = 0

Multiply (7m + -5n) * (2m + 5n)
(7m * (2m + 5n) + -5n * (2m + 5n)) = 0
((2m * 7m + 5n * 7m) + -5n * (2m + 5n)) = 0

Reorder the terms:
((35mn + 14m2) + -5n * (2m + 5n)) = 0
((35mn + 14m2) + -5n * (2m + 5n)) = 0
(35mn + 14m2 + (2m * -5n + 5n * -5n)) = 0
(35mn + 14m2 + (-10mn + -25n2)) = 0

Reorder the terms:
(35mn + -10mn + 14m2 + -25n2) = 0

Combine like terms: 35mn + -10mn = 25mn
(25mn + 14m2 + -25n2) = 0

Solving
25mn + 14m2 + -25n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(7m + -5n)(2m + 5n) = 0


Subproblem 1
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

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

Simplifying
2m + 5n = 0

Solving
2m + 5n = 0

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

Add '-5n' to each side of the equation.
2m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
2m + 0 = 0 + -5n
2m = 0 + -5n
Remove the zero:
2m = -5n

Divide each side by '2'.
m = -2.5n

Simplifying
m = -2.5n
Solution
m = {0.7142857143n, -2.5n}

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