N(n-5)+n(n+8)=n(n-13)+n(n+1)+16

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Solution for N(n-5)+n(n+8)=n(n-13)+n(n+1)+16 equation: 


Simplifying
N(n + -5) + n(n + 8) = n(n + -13) + n(n + 1) + 16

Reorder the terms:
N(-5 + n) + n(n + 8) = n(n + -13) + n(n + 1) + 16
(-5 * N + n * N) + n(n + 8) = n(n + -13) + n(n + 1) + 16
(-5N + nN) + n(n + 8) = n(n + -13) + n(n + 1) + 16

Reorder the terms:
-5N + nN + n(8 + n) = n(n + -13) + n(n + 1) + 16
-5N + nN + (8 * n + n * n) = n(n + -13) + n(n + 1) + 16
-5N + nN + (8n + n2) = n(n + -13) + n(n + 1) + 16

Reorder the terms:
-5N + 8n + nN + n2 = n(n + -13) + n(n + 1) + 16

Reorder the terms:
-5N + 8n + nN + n2 = n(-13 + n) + n(n + 1) + 16
-5N + 8n + nN + n2 = (-13 * n + n * n) + n(n + 1) + 16
-5N + 8n + nN + n2 = (-13n + n2) + n(n + 1) + 16

Reorder the terms:
-5N + 8n + nN + n2 = -13n + n2 + n(1 + n) + 16
-5N + 8n + nN + n2 = -13n + n2 + (1 * n + n * n) + 16
-5N + 8n + nN + n2 = -13n + n2 + (1n + n2) + 16

Reorder the terms:
-5N + 8n + nN + n2 = 16 + -13n + 1n + n2 + n2

Combine like terms: -13n + 1n = -12n
-5N + 8n + nN + n2 = 16 + -12n + n2 + n2

Combine like terms: n2 + n2 = 2n2
-5N + 8n + nN + n2 = 16 + -12n + 2n2

Solving
-5N + 8n + nN + n2 = 16 + -12n + 2n2

Solving for variable 'N'.

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

Add '-8n' to each side of the equation.
-5N + 8n + nN + -8n + n2 = 16 + -12n + -8n + 2n2

Reorder the terms:
-5N + 8n + -8n + nN + n2 = 16 + -12n + -8n + 2n2

Combine like terms: 8n + -8n = 0
-5N + 0 + nN + n2 = 16 + -12n + -8n + 2n2
-5N + nN + n2 = 16 + -12n + -8n + 2n2

Combine like terms: -12n + -8n = -20n
-5N + nN + n2 = 16 + -20n + 2n2

Add '-1n2' to each side of the equation.
-5N + nN + n2 + -1n2 = 16 + -20n + 2n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-5N + nN + 0 = 16 + -20n + 2n2 + -1n2
-5N + nN = 16 + -20n + 2n2 + -1n2

Combine like terms: 2n2 + -1n2 = 1n2
-5N + nN = 16 + -20n + 1n2

Reorder the terms:
-16 + -5N + 20n + nN + -1n2 = 16 + -20n + 1n2 + -16 + 20n + -1n2

Reorder the terms:
-16 + -5N + 20n + nN + -1n2 = 16 + -16 + -20n + 20n + 1n2 + -1n2

Combine like terms: 16 + -16 = 0
-16 + -5N + 20n + nN + -1n2 = 0 + -20n + 20n + 1n2 + -1n2
-16 + -5N + 20n + nN + -1n2 = -20n + 20n + 1n2 + -1n2

Combine like terms: -20n + 20n = 0
-16 + -5N + 20n + nN + -1n2 = 0 + 1n2 + -1n2
-16 + -5N + 20n + nN + -1n2 = 1n2 + -1n2

Combine like terms: 1n2 + -1n2 = 0
-16 + -5N + 20n + nN + -1n2 = 0

The solution to this equation could not be determined.

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