(10m-2n)(6m+10n)=

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Solution for (10m-2n)(6m+10n)= equation: 


Simplifying
(10m + -2n)(6m + 10n) = 0

Multiply (10m + -2n) * (6m + 10n)
(10m * (6m + 10n) + -2n * (6m + 10n)) = 0
((6m * 10m + 10n * 10m) + -2n * (6m + 10n)) = 0

Reorder the terms:
((100mn + 60m2) + -2n * (6m + 10n)) = 0
((100mn + 60m2) + -2n * (6m + 10n)) = 0
(100mn + 60m2 + (6m * -2n + 10n * -2n)) = 0
(100mn + 60m2 + (-12mn + -20n2)) = 0

Reorder the terms:
(100mn + -12mn + 60m2 + -20n2) = 0

Combine like terms: 100mn + -12mn = 88mn
(88mn + 60m2 + -20n2) = 0

Solving
88mn + 60m2 + -20n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(22mn + 15m2 + -5n2) = 0

Factor a trinomial.
4((5m + -1n)(3m + 5n)) = 0

Ignore the factor 4.

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

Simplifying
5m + -1n = 0

Solving
5m + -1n = 0

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

Add 'n' to each side of the equation.
5m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
5m + 0 = 0 + n
5m = 0 + n
Remove the zero:
5m = n

Divide each side by '5'.
m = 0.2n

Simplifying
m = 0.2n

Subproblem 2
Set the factor '(3m + 5n)' equal to zero and attempt to solve:

Simplifying
3m + 5n = 0

Solving
3m + 5n = 0

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

Add '-5n' to each side of the equation.
3m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
3m + 0 = 0 + -5n
3m = 0 + -5n
Remove the zero:
3m = -5n

Divide each side by '3'.
m = -1.666666667n

Simplifying
m = -1.666666667n
Solution
m = {0.2n, -1.666666667n}

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