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

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


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

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

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

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

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

Solving
-64 + 8n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 4n + n2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-8, 4}

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