(8m-4n)(6m+9n)=

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Solution for (8m-4n)(6m+9n)= equation: 


Simplifying
(8m + -4n)(6m + 9n) = 0

Multiply (8m + -4n) * (6m + 9n)
(8m * (6m + 9n) + -4n * (6m + 9n)) = 0
((6m * 8m + 9n * 8m) + -4n * (6m + 9n)) = 0

Reorder the terms:
((72mn + 48m2) + -4n * (6m + 9n)) = 0
((72mn + 48m2) + -4n * (6m + 9n)) = 0
(72mn + 48m2 + (6m * -4n + 9n * -4n)) = 0
(72mn + 48m2 + (-24mn + -36n2)) = 0

Reorder the terms:
(72mn + -24mn + 48m2 + -36n2) = 0

Combine like terms: 72mn + -24mn = 48mn
(48mn + 48m2 + -36n2) = 0

Solving
48mn + 48m2 + -36n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '12'.
12(4mn + 4m2 + -3n2) = 0

Factor a trinomial.
12((2m + -1n)(2m + 3n)) = 0

Ignore the factor 12.

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 '(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
Solution
m = {0.5n, -1.5n}

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