(7m-3n)(6m+7n)=

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Solution for (7m-3n)(6m+7n)= equation: 


Simplifying
(7m + -3n)(6m + 7n) = 0

Multiply (7m + -3n) * (6m + 7n)
(7m * (6m + 7n) + -3n * (6m + 7n)) = 0
((6m * 7m + 7n * 7m) + -3n * (6m + 7n)) = 0

Reorder the terms:
((49mn + 42m2) + -3n * (6m + 7n)) = 0
((49mn + 42m2) + -3n * (6m + 7n)) = 0
(49mn + 42m2 + (6m * -3n + 7n * -3n)) = 0
(49mn + 42m2 + (-18mn + -21n2)) = 0

Reorder the terms:
(49mn + -18mn + 42m2 + -21n2) = 0

Combine like terms: 49mn + -18mn = 31mn
(31mn + 42m2 + -21n2) = 0

Solving
31mn + 42m2 + -21n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(7m + -3n)(6m + 7n) = 0


Subproblem 1
Set the factor '(7m + -3n)' equal to zero and attempt to solve:

Simplifying
7m + -3n = 0

Solving
7m + -3n = 0

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

Add '3n' to each side of the equation.
7m + -3n + 3n = 0 + 3n

Combine like terms: -3n + 3n = 0
7m + 0 = 0 + 3n
7m = 0 + 3n
Remove the zero:
7m = 3n

Divide each side by '7'.
m = 0.4285714286n

Simplifying
m = 0.4285714286n

Subproblem 2
Set the factor '(6m + 7n)' equal to zero and attempt to solve:

Simplifying
6m + 7n = 0

Solving
6m + 7n = 0

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

Add '-7n' to each side of the equation.
6m + 7n + -7n = 0 + -7n

Combine like terms: 7n + -7n = 0
6m + 0 = 0 + -7n
6m = 0 + -7n
Remove the zero:
6m = -7n

Divide each side by '6'.
m = -1.166666667n

Simplifying
m = -1.166666667n
Solution
m = {0.4285714286n, -1.166666667n}

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