A(n)=n(2n-8)

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Solution for A(n)=n(2n-8) equation: 


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

Multiply A * n
nA = n(2n + -8)

Reorder the terms:
nA = n(-8 + 2n)
nA = (-8 * n + 2n * n)
nA = (-8n + 2n2)

Solving
nA = -8n + 2n2

Solving for variable 'n'.

Reorder the terms:
8n + nA + -2n2 = -8n + 2n2 + 8n + -2n2

Reorder the terms:
8n + nA + -2n2 = -8n + 8n + 2n2 + -2n2

Combine like terms: -8n + 8n = 0
8n + nA + -2n2 = 0 + 2n2 + -2n2
8n + nA + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
8n + nA + -2n2 = 0

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


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

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

Simplifying
8 + A + -2n = 0

Solving
8 + A + -2n = 0

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

Add '-8' to each side of the equation.
8 + A + -8 + -2n = 0 + -8

Reorder the terms:
8 + -8 + A + -2n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + A + -2n = 0 + -8
A + -2n = 0 + -8

Combine like terms: 0 + -8 = -8
A + -2n = -8

Add '-1A' to each side of the equation.
A + -1A + -2n = -8 + -1A

Combine like terms: A + -1A = 0
0 + -2n = -8 + -1A
-2n = -8 + -1A

Divide each side by '-2'.
n = 4 + 0.5A

Simplifying
n = 4 + 0.5A
Solution
n = {0, 4 + 0.5A}

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