0=-256+224n-24n^2

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Solution for 0=-256+224n-24n^2 equation: 


Simplifying
0 = -256 + 224n + -24n2

Solving
0 = -256 + 224n + -24n2

Solving for variable 'n'.

Combine like terms: 0 + 256 = 256
256 + -224n + 24n2 = -256 + 224n + -24n2 + 256 + -224n + 24n2

Reorder the terms:
256 + -224n + 24n2 = -256 + 256 + 224n + -224n + -24n2 + 24n2

Combine like terms: -256 + 256 = 0
256 + -224n + 24n2 = 0 + 224n + -224n + -24n2 + 24n2
256 + -224n + 24n2 = 224n + -224n + -24n2 + 24n2

Combine like terms: 224n + -224n = 0
256 + -224n + 24n2 = 0 + -24n2 + 24n2
256 + -224n + 24n2 = -24n2 + 24n2

Combine like terms: -24n2 + 24n2 = 0
256 + -224n + 24n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(32 + -28n + 3n2) = 0

Factor a trinomial.
8((4 + -3n)(8 + -1n)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 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 + -3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n = 0 + -4
-3n = 0 + -4

Combine like terms: 0 + -4 = -4
-3n = -4

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333

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 = {1.333333333, 8}

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