n(n-4)+n(n+8)=n(n-13)+n(n+1)16

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Solution for n(n-4)+n(n+8)=n(n-13)+n(n+1)16 equation: 


Simplifying
n(n + -4) + n(n + 8) = n(n + -13) + n(n + 1) * 16

Reorder the terms:
n(-4 + n) + n(n + 8) = n(n + -13) + n(n + 1) * 16
(-4 * n + n * n) + n(n + 8) = n(n + -13) + n(n + 1) * 16
(-4n + n2) + n(n + 8) = n(n + -13) + n(n + 1) * 16

Reorder the terms:
-4n + n2 + n(8 + n) = n(n + -13) + n(n + 1) * 16
-4n + n2 + (8 * n + n * n) = n(n + -13) + n(n + 1) * 16
-4n + n2 + (8n + n2) = n(n + -13) + n(n + 1) * 16

Reorder the terms:
-4n + 8n + n2 + n2 = n(n + -13) + n(n + 1) * 16

Combine like terms: -4n + 8n = 4n
4n + n2 + n2 = n(n + -13) + n(n + 1) * 16

Combine like terms: n2 + n2 = 2n2
4n + 2n2 = n(n + -13) + n(n + 1) * 16

Reorder the terms:
4n + 2n2 = n(-13 + n) + n(n + 1) * 16
4n + 2n2 = (-13 * n + n * n) + n(n + 1) * 16
4n + 2n2 = (-13n + n2) + n(n + 1) * 16

Reorder the terms:
4n + 2n2 = -13n + n2 + n(1 + n) * 16

Reorder the terms for easier multiplication:
4n + 2n2 = -13n + n2 + 16n(1 + n)
4n + 2n2 = -13n + n2 + (1 * 16n + n * 16n)
4n + 2n2 = -13n + n2 + (16n + 16n2)

Reorder the terms:
4n + 2n2 = -13n + 16n + n2 + 16n2

Combine like terms: -13n + 16n = 3n
4n + 2n2 = 3n + n2 + 16n2

Combine like terms: n2 + 16n2 = 17n2
4n + 2n2 = 3n + 17n2

Solving
4n + 2n2 = 3n + 17n2

Solving for variable 'n'.

Reorder the terms:
4n + -3n + 2n2 + -17n2 = 3n + 17n2 + -3n + -17n2

Combine like terms: 4n + -3n = 1n
1n + 2n2 + -17n2 = 3n + 17n2 + -3n + -17n2

Combine like terms: 2n2 + -17n2 = -15n2
1n + -15n2 = 3n + 17n2 + -3n + -17n2

Reorder the terms:
1n + -15n2 = 3n + -3n + 17n2 + -17n2

Combine like terms: 3n + -3n = 0
1n + -15n2 = 0 + 17n2 + -17n2
1n + -15n2 = 17n2 + -17n2

Combine like terms: 17n2 + -17n2 = 0
1n + -15n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + -15n) = 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 '(1 + -15n)' equal to zero and attempt to solve:

Simplifying
1 + -15n = 0

Solving
1 + -15n = 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 + -15n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -15n = 0 + -1
-15n = 0 + -1

Combine like terms: 0 + -1 = -1
-15n = -1

Divide each side by '-15'.
n = 0.06666666667

Simplifying
n = 0.06666666667
Solution
n = {0, 0.06666666667}

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