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

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


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

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

Reorder the terms:
((48mn + 18m2) + -3n * (3m + 8n)) = 0
((48mn + 18m2) + -3n * (3m + 8n)) = 0
(48mn + 18m2 + (3m * -3n + 8n * -3n)) = 0
(48mn + 18m2 + (-9mn + -24n2)) = 0

Reorder the terms:
(48mn + -9mn + 18m2 + -24n2) = 0

Combine like terms: 48mn + -9mn = 39mn
(39mn + 18m2 + -24n2) = 0

Solving
39mn + 18m2 + -24n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(13mn + 6m2 + -8n2) = 0

Factor a trinomial.
3((2m + -1n)(3m + 8n)) = 0

Ignore the factor 3.

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

Simplifying
2m + -1n = 0

Solving
2m + -1n = 0

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

Add 'n' to each side of the equation.
2m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
2m + 0 = 0 + n
2m = 0 + n
Remove the zero:
2m = n

Divide each side by '2'.
m = 0.5n

Simplifying
m = 0.5n

Subproblem 2
Set the factor '(3m + 8n)' equal to zero and attempt to solve:

Simplifying
3m + 8n = 0

Solving
3m + 8n = 0

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

Add '-8n' to each side of the equation.
3m + 8n + -8n = 0 + -8n

Combine like terms: 8n + -8n = 0
3m + 0 = 0 + -8n
3m = 0 + -8n
Remove the zero:
3m = -8n

Divide each side by '3'.
m = -2.666666667n

Simplifying
m = -2.666666667n
Solution
m = {0.5n, -2.666666667n}

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