(n+2)(n+1)(n+6)-9n^2=n^3+4(7n-1)

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Solution for (n+2)(n+1)(n+6)-9n^2=n^3+4(7n-1) equation: 


Simplifying
(n + 2)(n + 1)(n + 6) + -9n2 = n3 + 4(7n + -1)

Reorder the terms:
(2 + n)(n + 1)(n + 6) + -9n2 = n3 + 4(7n + -1)

Reorder the terms:
(2 + n)(1 + n)(n + 6) + -9n2 = n3 + 4(7n + -1)

Reorder the terms:
(2 + n)(1 + n)(6 + n) + -9n2 = n3 + 4(7n + -1)

Multiply (2 + n) * (1 + n)
(2(1 + n) + n(1 + n))(6 + n) + -9n2 = n3 + 4(7n + -1)
((1 * 2 + n * 2) + n(1 + n))(6 + n) + -9n2 = n3 + 4(7n + -1)
((2 + 2n) + n(1 + n))(6 + n) + -9n2 = n3 + 4(7n + -1)
(2 + 2n + (1 * n + n * n))(6 + n) + -9n2 = n3 + 4(7n + -1)
(2 + 2n + (1n + n2))(6 + n) + -9n2 = n3 + 4(7n + -1)

Combine like terms: 2n + 1n = 3n
(2 + 3n + n2)(6 + n) + -9n2 = n3 + 4(7n + -1)

Multiply (2 + 3n + n2) * (6 + n)
(2(6 + n) + 3n * (6 + n) + n2(6 + n)) + -9n2 = n3 + 4(7n + -1)
((6 * 2 + n * 2) + 3n * (6 + n) + n2(6 + n)) + -9n2 = n3 + 4(7n + -1)
((12 + 2n) + 3n * (6 + n) + n2(6 + n)) + -9n2 = n3 + 4(7n + -1)
(12 + 2n + (6 * 3n + n * 3n) + n2(6 + n)) + -9n2 = n3 + 4(7n + -1)
(12 + 2n + (18n + 3n2) + n2(6 + n)) + -9n2 = n3 + 4(7n + -1)
(12 + 2n + 18n + 3n2 + (6 * n2 + n * n2)) + -9n2 = n3 + 4(7n + -1)
(12 + 2n + 18n + 3n2 + (6n2 + n3)) + -9n2 = n3 + 4(7n + -1)

Combine like terms: 2n + 18n = 20n
(12 + 20n + 3n2 + 6n2 + n3) + -9n2 = n3 + 4(7n + -1)

Combine like terms: 3n2 + 6n2 = 9n2
(12 + 20n + 9n2 + n3) + -9n2 = n3 + 4(7n + -1)

Reorder the terms:
12 + 20n + 9n2 + -9n2 + n3 = n3 + 4(7n + -1)

Combine like terms: 9n2 + -9n2 = 0
12 + 20n + 0 + n3 = n3 + 4(7n + -1)
12 + 20n + n3 = n3 + 4(7n + -1)

Reorder the terms:
12 + 20n + n3 = n3 + 4(-1 + 7n)
12 + 20n + n3 = n3 + (-1 * 4 + 7n * 4)
12 + 20n + n3 = n3 + (-4 + 28n)

Reorder the terms:
12 + 20n + n3 = -4 + 28n + n3

Add '-1n3' to each side of the equation.
12 + 20n + n3 + -1n3 = -4 + 28n + n3 + -1n3

Combine like terms: n3 + -1n3 = 0
12 + 20n + 0 = -4 + 28n + n3 + -1n3
12 + 20n = -4 + 28n + n3 + -1n3

Combine like terms: n3 + -1n3 = 0
12 + 20n = -4 + 28n + 0
12 + 20n = -4 + 28n

Solving
12 + 20n = -4 + 28n

Solving for variable 'n'.

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

Add '-28n' to each side of the equation.
12 + 20n + -28n = -4 + 28n + -28n

Combine like terms: 20n + -28n = -8n
12 + -8n = -4 + 28n + -28n

Combine like terms: 28n + -28n = 0
12 + -8n = -4 + 0
12 + -8n = -4

Add '-12' to each side of the equation.
12 + -12 + -8n = -4 + -12

Combine like terms: 12 + -12 = 0
0 + -8n = -4 + -12
-8n = -4 + -12

Combine like terms: -4 + -12 = -16
-8n = -16

Divide each side by '-8'.
n = 2

Simplifying
n = 2

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