(10m-3n)(6m+8n)=

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Solution for (10m-3n)(6m+8n)= equation: 


Simplifying
(10m + -3n)(6m + 8n) = 0

Multiply (10m + -3n) * (6m + 8n)
(10m * (6m + 8n) + -3n * (6m + 8n)) = 0
((6m * 10m + 8n * 10m) + -3n * (6m + 8n)) = 0

Reorder the terms:
((80mn + 60m2) + -3n * (6m + 8n)) = 0
((80mn + 60m2) + -3n * (6m + 8n)) = 0
(80mn + 60m2 + (6m * -3n + 8n * -3n)) = 0
(80mn + 60m2 + (-18mn + -24n2)) = 0

Reorder the terms:
(80mn + -18mn + 60m2 + -24n2) = 0

Combine like terms: 80mn + -18mn = 62mn
(62mn + 60m2 + -24n2) = 0

Solving
62mn + 60m2 + -24n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(31mn + 30m2 + -12n2) = 0

Factor a trinomial.
2((10m + -3n)(3m + 4n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10m + -3n)' equal to zero and attempt to solve:

Simplifying
10m + -3n = 0

Solving
10m + -3n = 0

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

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

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

Divide each side by '10'.
m = 0.3n

Simplifying
m = 0.3n

Subproblem 2
Set the factor '(3m + 4n)' equal to zero and attempt to solve:

Simplifying
3m + 4n = 0

Solving
3m + 4n = 0

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

Add '-4n' to each side of the equation.
3m + 4n + -4n = 0 + -4n

Combine like terms: 4n + -4n = 0
3m + 0 = 0 + -4n
3m = 0 + -4n
Remove the zero:
3m = -4n

Divide each side by '3'.
m = -1.333333333n

Simplifying
m = -1.333333333n
Solution
m = {0.3n, -1.333333333n}

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