n^2-2nx-8x^2=0

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Solution for n^2-2nx-8x^2=0 equation: 


Simplifying
n2 + -2nx + -8x2 = 0

Reorder the terms:
-2nx + n2 + -8x2 = 0

Solving
-2nx + n2 + -8x2 = 0

Solving for variable 'n'.

Factor a trinomial.
(n + -4x)(n + 2x) = 0


Subproblem 1
Set the factor '(n + -4x)' equal to zero and attempt to solve:

Simplifying
n + -4x = 0

Solving
n + -4x = 0

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

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

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

Simplifying
n = 4x

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

Simplifying
n + 2x = 0

Solving
n + 2x = 0

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

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

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

Simplifying
n = -2x
Solution
n = {4x, -2x}

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