(-n+8)(-8n-2)=0

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Solution for (-n+8)(-8n-2)=0 equation: 


Simplifying
(-1n + 8)(-8n + -2) = 0

Reorder the terms:
(8 + -1n)(-8n + -2) = 0

Reorder the terms:
(8 + -1n)(-2 + -8n) = 0

Multiply (8 + -1n) * (-2 + -8n)
(8(-2 + -8n) + -1n * (-2 + -8n)) = 0
((-2 * 8 + -8n * 8) + -1n * (-2 + -8n)) = 0
((-16 + -64n) + -1n * (-2 + -8n)) = 0
(-16 + -64n + (-2 * -1n + -8n * -1n)) = 0
(-16 + -64n + (2n + 8n2)) = 0

Combine like terms: -64n + 2n = -62n
(-16 + -62n + 8n2) = 0

Solving
-16 + -62n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -31n + 4n2) = 0

Factor a trinomial.
2((-1 + -4n)(8 + -1n)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -4n = 0

Solving
-1 + -4n = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -4n = 0 + 1
-4n = 0 + 1

Combine like terms: 0 + 1 = 1
-4n = 1

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

Simplifying
n = -0.25

Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-0.25, 8}

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