(2s-2xn)(4s+2xn)=

Solution for (2s-2xn)(4s+2xn)= equation:

Simplifying
(2s + -2xn)(4s + 2xn) = 0

Reorder the terms:
(-2nx + 2s)(4s + 2xn) = 0

Reorder the terms:
(-2nx + 2s)(2nx + 4s) = 0

Multiply (-2nx + 2s) * (2nx + 4s)
(-2nx * (2nx + 4s) + 2s * (2nx + 4s)) = 0
((2nx * -2nx + 4s * -2nx) + 2s * (2nx + 4s)) = 0

Reorder the terms:
((-8nsx + -4n2x2) + 2s * (2nx + 4s)) = 0
((-8nsx + -4n2x2) + 2s * (2nx + 4s)) = 0
(-8nsx + -4n2x2 + (2nx * 2s + 4s * 2s)) = 0
(-8nsx + -4n2x2 + (4nsx + 8s2)) = 0

Reorder the terms:
(-8nsx + 4nsx + -4n2x2 + 8s2) = 0

Combine like terms: -8nsx + 4nsx = -4nsx
(-4nsx + -4n2x2 + 8s2) = 0

Solving
-4nsx + -4n2x2 + 8s2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1nsx + -1n2x2 + 2s2) = 0

Factor a trinomial.
4((-1nx + -2s)(nx + -1s)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1nx + -2s)' equal to zero and attempt to solve:

Simplifying
-1nx + -2s = 0

Solving
-1nx + -2s = 0

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

Add '2s' to each side of the equation.
-1nx + -2s + 2s = 0 + 2s

Combine like terms: -2s + 2s = 0
-1nx + 0 = 0 + 2s
-1nx = 0 + 2s
Remove the zero:
-1nx = 2s

Divide each side by '-1x'.
n = -2sx-1

Simplifying
n = -2sx-1
Subproblem 2
Set the factor '(nx + -1s)' equal to zero and attempt to solve:

Simplifying
nx + -1s = 0

Solving
nx + -1s = 0

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

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

Combine like terms: -1s + s = 0
nx + 0 = 0 + s
nx = 0 + s
Remove the zero:
nx = s

Divide each side by 'x'.
n = sx-1

Simplifying
n = sx-1
Solution
n = {-2sx-1, sx-1}