(mn^2+n)(5mn^2-n)=

Solution for (mn^2+n)(5mn^2-n)= equation:

Simplifying
(mn2 + n)(5mn2 + -1n) = 0

Multiply (mn2 + n) * (5mn2 + -1n)
(mn2(5mn2 + -1n) + n(5mn2 + -1n)) = 0
((5mn2 * mn2 + -1n * mn2) + n(5mn2 + -1n)) = 0

Reorder the terms:
((-1mn3 + 5m2n4) + n(5mn2 + -1n)) = 0
((-1mn3 + 5m2n4) + n(5mn2 + -1n)) = 0
(-1mn3 + 5m2n4 + (5mn2 * n + -1n * n)) = 0
(-1mn3 + 5m2n4 + (5mn3 + -1n2)) = 0

Reorder the terms:
(-1mn3 + 5mn3 + 5m2n4 + -1n2) = 0

Combine like terms: -1mn3 + 5mn3 = 4mn3
(4mn3 + 5m2n4 + -1n2) = 0

Solving
4mn3 + 5m2n4 + -1n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(4mn + 5m2n2 + -1) = 0

Factor a trinomial.
n2((5mn + -1)(mn + 1)) = 0

Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Add '-1n2' to each side of the equation.
n2 + -1n2 = 0 + -1n2
Remove the zero:
0 = -1n2

Simplifying
0 = -1n2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(5mn + -1)' equal to zero and attempt to solve:

Simplifying
5mn + -1 = 0

Reorder the terms:
-1 + 5mn = 0

Solving
-1 + 5mn = 0

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

Add '1' to each side of the equation.
-1 + 1 + 5mn = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5mn = 0 + 1
5mn = 0 + 1

Combine like terms: 0 + 1 = 1
5mn = 1

Divide each side by '5n'.
m = 0.2n-1

Simplifying
m = 0.2n-1
Subproblem 3
Set the factor '(mn + 1)' equal to zero and attempt to solve:

Simplifying
mn + 1 = 0

Reorder the terms:
1 + mn = 0

Solving
1 + mn = 0

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

Add '-1' to each side of the equation.
1 + -1 + mn = 0 + -1

Combine like terms: 1 + -1 = 0
0 + mn = 0 + -1
mn = 0 + -1

Combine like terms: 0 + -1 = -1
mn = -1

Divide each side by 'n'.
m = -1n-1

Simplifying
m = -1n-1
Solution
m = {0.2n-1, -1n-1}