(z+5n)(z-4n)=

Solution for (z+5n)(z-4n)= equation:

Simplifying
(z + 5n)(z + -4n) = 0

Reorder the terms:
(5n + z)(z + -4n) = 0

Reorder the terms:
(5n + z)(-4n + z) = 0

Multiply (5n + z) * (-4n + z)
(5n * (-4n + z) + z(-4n + z)) = 0
((-4n * 5n + z * 5n) + z(-4n + z)) = 0

Reorder the terms:
((5nz + -20n2) + z(-4n + z)) = 0
((5nz + -20n2) + z(-4n + z)) = 0
(5nz + -20n2 + (-4n * z + z * z)) = 0
(5nz + -20n2 + (-4nz + z2)) = 0

Reorder the terms:
(5nz + -4nz + -20n2 + z2) = 0

Combine like terms: 5nz + -4nz = 1nz
(1nz + -20n2 + z2) = 0

Solving
1nz + -20n2 + z2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5n + -1z)(4n + -1z) = 0

Subproblem 1
Set the factor '(-5n + -1z)' equal to zero and attempt to solve:

Simplifying
-5n + -1z = 0

Solving
-5n + -1z = 0

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

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

Combine like terms: -1z + z = 0
-5n + 0 = 0 + z
-5n = 0 + z
Remove the zero:
-5n = z

Divide each side by '-5'.
n = -0.2z

Simplifying
n = -0.2z
Subproblem 2
Set the factor '(4n + -1z)' equal to zero and attempt to solve:

Simplifying
4n + -1z = 0

Solving
4n + -1z = 0

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

Add 'z' to each side of the equation.
4n + -1z + z = 0 + z

Combine like terms: -1z + z = 0
4n + 0 = 0 + z
4n = 0 + z
Remove the zero:
4n = z

Divide each side by '4'.
n = 0.25z

Simplifying
n = 0.25z
Solution
n = {-0.2z, 0.25z}