5m(2m-3n)-7n(2m-3n)=

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Solution for 5m(2m-3n)-7n(2m-3n)= equation: 


Simplifying
5m(2m + -3n) + -7n(2m + -3n) = 0
(2m * 5m + -3n * 5m) + -7n(2m + -3n) = 0

Reorder the terms:
(-15mn + 10m2) + -7n(2m + -3n) = 0
(-15mn + 10m2) + -7n(2m + -3n) = 0
-15mn + 10m2 + (2m * -7n + -3n * -7n) = 0
-15mn + 10m2 + (-14mn + 21n2) = 0

Reorder the terms:
-15mn + -14mn + 10m2 + 21n2 = 0

Combine like terms: -15mn + -14mn = -29mn
-29mn + 10m2 + 21n2 = 0

Solving
-29mn + 10m2 + 21n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2m + -3n)(5m + -7n) = 0


Subproblem 1
Set the factor '(2m + -3n)' equal to zero and attempt to solve:

Simplifying
2m + -3n = 0

Solving
2m + -3n = 0

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

Add '3n' to each side of the equation.
2m + -3n + 3n = 0 + 3n

Combine like terms: -3n + 3n = 0
2m + 0 = 0 + 3n
2m = 0 + 3n
Remove the zero:
2m = 3n

Divide each side by '2'.
m = 1.5n

Simplifying
m = 1.5n

Subproblem 2
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
Solution
m = {1.5n, 1.4n}

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