(5m-2n)(3m+10n)=

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Solution for (5m-2n)(3m+10n)= equation: 


Simplifying
(5m + -2n)(3m + 10n) = 0

Multiply (5m + -2n) * (3m + 10n)
(5m * (3m + 10n) + -2n * (3m + 10n)) = 0
((3m * 5m + 10n * 5m) + -2n * (3m + 10n)) = 0

Reorder the terms:
((50mn + 15m2) + -2n * (3m + 10n)) = 0
((50mn + 15m2) + -2n * (3m + 10n)) = 0
(50mn + 15m2 + (3m * -2n + 10n * -2n)) = 0
(50mn + 15m2 + (-6mn + -20n2)) = 0

Reorder the terms:
(50mn + -6mn + 15m2 + -20n2) = 0

Combine like terms: 50mn + -6mn = 44mn
(44mn + 15m2 + -20n2) = 0

Solving
44mn + 15m2 + -20n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(5m + -2n)(3m + 10n) = 0


Subproblem 1
Set the factor '(5m + -2n)' equal to zero and attempt to solve:

Simplifying
5m + -2n = 0

Solving
5m + -2n = 0

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

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

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

Divide each side by '5'.
m = 0.4n

Simplifying
m = 0.4n

Subproblem 2
Set the factor '(3m + 10n)' equal to zero and attempt to solve:

Simplifying
3m + 10n = 0

Solving
3m + 10n = 0

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

Add '-10n' to each side of the equation.
3m + 10n + -10n = 0 + -10n

Combine like terms: 10n + -10n = 0
3m + 0 = 0 + -10n
3m = 0 + -10n
Remove the zero:
3m = -10n

Divide each side by '3'.
m = -3.333333333n

Simplifying
m = -3.333333333n
Solution
m = {0.4n, -3.333333333n}

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