(7m-4n)(6m+10n)=

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Solution for (7m-4n)(6m+10n)= equation: 


Simplifying
(7m + -4n)(6m + 10n) = 0

Multiply (7m + -4n) * (6m + 10n)
(7m * (6m + 10n) + -4n * (6m + 10n)) = 0
((6m * 7m + 10n * 7m) + -4n * (6m + 10n)) = 0

Reorder the terms:
((70mn + 42m2) + -4n * (6m + 10n)) = 0
((70mn + 42m2) + -4n * (6m + 10n)) = 0
(70mn + 42m2 + (6m * -4n + 10n * -4n)) = 0
(70mn + 42m2 + (-24mn + -40n2)) = 0

Reorder the terms:
(70mn + -24mn + 42m2 + -40n2) = 0

Combine like terms: 70mn + -24mn = 46mn
(46mn + 42m2 + -40n2) = 0

Solving
46mn + 42m2 + -40n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(23mn + 21m2 + -20n2) = 0

Factor a trinomial.
2((7m + -4n)(3m + 5n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7m + -4n)' equal to zero and attempt to solve:

Simplifying
7m + -4n = 0

Solving
7m + -4n = 0

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

Add '4n' to each side of the equation.
7m + -4n + 4n = 0 + 4n

Combine like terms: -4n + 4n = 0
7m + 0 = 0 + 4n
7m = 0 + 4n
Remove the zero:
7m = 4n

Divide each side by '7'.
m = 0.5714285714n

Simplifying
m = 0.5714285714n

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 = {0.5714285714n, -1.666666667n}

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