(7m+5n)(2m-9n)=

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Solution for (7m+5n)(2m-9n)= equation: 


Simplifying
(7m + 5n)(2m + -9n) = 0

Multiply (7m + 5n) * (2m + -9n)
(7m * (2m + -9n) + 5n * (2m + -9n)) = 0
((2m * 7m + -9n * 7m) + 5n * (2m + -9n)) = 0

Reorder the terms:
((-63mn + 14m2) + 5n * (2m + -9n)) = 0
((-63mn + 14m2) + 5n * (2m + -9n)) = 0
(-63mn + 14m2 + (2m * 5n + -9n * 5n)) = 0
(-63mn + 14m2 + (10mn + -45n2)) = 0

Reorder the terms:
(-63mn + 10mn + 14m2 + -45n2) = 0

Combine like terms: -63mn + 10mn = -53mn
(-53mn + 14m2 + -45n2) = 0

Solving
-53mn + 14m2 + -45n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2m + -9n)(7m + 5n) = 0


Subproblem 1
Set the factor '(2m + -9n)' equal to zero and attempt to solve:

Simplifying
2m + -9n = 0

Solving
2m + -9n = 0

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

Add '9n' to each side of the equation.
2m + -9n + 9n = 0 + 9n

Combine like terms: -9n + 9n = 0
2m + 0 = 0 + 9n
2m = 0 + 9n
Remove the zero:
2m = 9n

Divide each side by '2'.
m = 4.5n

Simplifying
m = 4.5n

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 = {4.5n, -0.7142857143n}

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