(8m+3n)(2m+5n)=

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Solution for (8m+3n)(2m+5n)= equation: 


Simplifying
(8m + 3n)(2m + 5n) = 0

Multiply (8m + 3n) * (2m + 5n)
(8m * (2m + 5n) + 3n * (2m + 5n)) = 0
((2m * 8m + 5n * 8m) + 3n * (2m + 5n)) = 0

Reorder the terms:
((40mn + 16m2) + 3n * (2m + 5n)) = 0
((40mn + 16m2) + 3n * (2m + 5n)) = 0
(40mn + 16m2 + (2m * 3n + 5n * 3n)) = 0
(40mn + 16m2 + (6mn + 15n2)) = 0

Reorder the terms:
(40mn + 6mn + 16m2 + 15n2) = 0

Combine like terms: 40mn + 6mn = 46mn
(46mn + 16m2 + 15n2) = 0

Solving
46mn + 16m2 + 15n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(8m + 3n)(2m + 5n) = 0


Subproblem 1
Set the factor '(8m + 3n)' equal to zero and attempt to solve:

Simplifying
8m + 3n = 0

Solving
8m + 3n = 0

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

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

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

Divide each side by '8'.
m = -0.375n

Simplifying
m = -0.375n

Subproblem 2
Set the factor '(2m + 5n)' equal to zero and attempt to solve:

Simplifying
2m + 5n = 0

Solving
2m + 5n = 0

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

Add '-5n' to each side of the equation.
2m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
2m + 0 = 0 + -5n
2m = 0 + -5n
Remove the zero:
2m = -5n

Divide each side by '2'.
m = -2.5n

Simplifying
m = -2.5n
Solution
m = {-0.375n, -2.5n}

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