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
4n + 2n2 = -13n + n2 + (1 * n + n * n) + -16
4n + 2n2 = -13n + n2 + (1n + n2) + -16

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

Combine like terms: -13n + 1n = -12n
4n + 2n2 = -16 + -12n + n2 + n2

Combine like terms: n2 + n2 = 2n2
4n + 2n2 = -16 + -12n + 2n2

Add '-2n2' to each side of the equation.
4n + 2n2 + -2n2 = -16 + -12n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
4n + 0 = -16 + -12n + 2n2 + -2n2
4n = -16 + -12n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
4n = -16 + -12n + 0
4n = -16 + -12n

Solving
4n = -16 + -12n

Solving for variable 'n'.

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

Add '12n' to each side of the equation.
4n + 12n = -16 + -12n + 12n

Combine like terms: 4n + 12n = 16n
16n = -16 + -12n + 12n

Combine like terms: -12n + 12n = 0
16n = -16 + 0
16n = -16

Divide each side by '16'.
n = -1

Simplifying
n = -1

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