(7m+10n)(2m-400n)=

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Solution for (7m+10n)(2m-400n)= equation: 


Simplifying
(7m + 10n)(2m + -400n) = 0

Multiply (7m + 10n) * (2m + -400n)
(7m * (2m + -400n) + 10n * (2m + -400n)) = 0
((2m * 7m + -400n * 7m) + 10n * (2m + -400n)) = 0

Reorder the terms:
((-2800mn + 14m2) + 10n * (2m + -400n)) = 0
((-2800mn + 14m2) + 10n * (2m + -400n)) = 0
(-2800mn + 14m2 + (2m * 10n + -400n * 10n)) = 0
(-2800mn + 14m2 + (20mn + -4000n2)) = 0

Reorder the terms:
(-2800mn + 20mn + 14m2 + -4000n2) = 0

Combine like terms: -2800mn + 20mn = -2780mn
(-2780mn + 14m2 + -4000n2) = 0

Solving
-2780mn + 14m2 + -4000n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1390mn + 7m2 + -2000n2) = 0

Factor a trinomial.
2((m + -200n)(7m + 10n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(m + -200n)' equal to zero and attempt to solve:

Simplifying
m + -200n = 0

Solving
m + -200n = 0

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

Add '200n' to each side of the equation.
m + -200n + 200n = 0 + 200n

Combine like terms: -200n + 200n = 0
m + 0 = 0 + 200n
m = 0 + 200n
Remove the zero:
m = 200n

Simplifying
m = 200n

Subproblem 2
Set the factor '(7m + 10n)' equal to zero and attempt to solve:

Simplifying
7m + 10n = 0

Solving
7m + 10n = 0

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

Add '-10n' to each side of the equation.
7m + 10n + -10n = 0 + -10n

Combine like terms: 10n + -10n = 0
7m + 0 = 0 + -10n
7m = 0 + -10n
Remove the zero:
7m = -10n

Divide each side by '7'.
m = -1.428571429n

Simplifying
m = -1.428571429n
Solution
m = {200n, -1.428571429n}

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