(n+1)(2n^2+13n+18)=(n+1)(n+2)(2n+9)

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Solution for (n+1)(2n^2+13n+18)=(n+1)(n+2)(2n+9) equation: 


Simplifying
(n + 1)(2n2 + 13n + 18) = (n + 1)(n + 2)(2n + 9)

Reorder the terms:
(1 + n)(2n2 + 13n + 18) = (n + 1)(n + 2)(2n + 9)

Reorder the terms:
(1 + n)(18 + 13n + 2n2) = (n + 1)(n + 2)(2n + 9)

Multiply (1 + n) * (18 + 13n + 2n2)
(1(18 + 13n + 2n2) + n(18 + 13n + 2n2)) = (n + 1)(n + 2)(2n + 9)
((18 * 1 + 13n * 1 + 2n2 * 1) + n(18 + 13n + 2n2)) = (n + 1)(n + 2)(2n + 9)
((18 + 13n + 2n2) + n(18 + 13n + 2n2)) = (n + 1)(n + 2)(2n + 9)
(18 + 13n + 2n2 + (18 * n + 13n * n + 2n2 * n)) = (n + 1)(n + 2)(2n + 9)
(18 + 13n + 2n2 + (18n + 13n2 + 2n3)) = (n + 1)(n + 2)(2n + 9)

Reorder the terms:
(18 + 13n + 18n + 2n2 + 13n2 + 2n3) = (n + 1)(n + 2)(2n + 9)

Combine like terms: 13n + 18n = 31n
(18 + 31n + 2n2 + 13n2 + 2n3) = (n + 1)(n + 2)(2n + 9)

Combine like terms: 2n2 + 13n2 = 15n2
(18 + 31n + 15n2 + 2n3) = (n + 1)(n + 2)(2n + 9)

Reorder the terms:
18 + 31n + 15n2 + 2n3 = (1 + n)(n + 2)(2n + 9)

Reorder the terms:
18 + 31n + 15n2 + 2n3 = (1 + n)(2 + n)(2n + 9)

Reorder the terms:
18 + 31n + 15n2 + 2n3 = (1 + n)(2 + n)(9 + 2n)

Multiply (1 + n) * (2 + n)
18 + 31n + 15n2 + 2n3 = (1(2 + n) + n(2 + n))(9 + 2n)
18 + 31n + 15n2 + 2n3 = ((2 * 1 + n * 1) + n(2 + n))(9 + 2n)
18 + 31n + 15n2 + 2n3 = ((2 + 1n) + n(2 + n))(9 + 2n)
18 + 31n + 15n2 + 2n3 = (2 + 1n + (2 * n + n * n))(9 + 2n)
18 + 31n + 15n2 + 2n3 = (2 + 1n + (2n + n2))(9 + 2n)

Combine like terms: 1n + 2n = 3n
18 + 31n + 15n2 + 2n3 = (2 + 3n + n2)(9 + 2n)

Multiply (2 + 3n + n2) * (9 + 2n)
18 + 31n + 15n2 + 2n3 = (2(9 + 2n) + 3n * (9 + 2n) + n2(9 + 2n))
18 + 31n + 15n2 + 2n3 = ((9 * 2 + 2n * 2) + 3n * (9 + 2n) + n2(9 + 2n))
18 + 31n + 15n2 + 2n3 = ((18 + 4n) + 3n * (9 + 2n) + n2(9 + 2n))
18 + 31n + 15n2 + 2n3 = (18 + 4n + (9 * 3n + 2n * 3n) + n2(9 + 2n))
18 + 31n + 15n2 + 2n3 = (18 + 4n + (27n + 6n2) + n2(9 + 2n))
18 + 31n + 15n2 + 2n3 = (18 + 4n + 27n + 6n2 + (9 * n2 + 2n * n2))
18 + 31n + 15n2 + 2n3 = (18 + 4n + 27n + 6n2 + (9n2 + 2n3))

Combine like terms: 4n + 27n = 31n
18 + 31n + 15n2 + 2n3 = (18 + 31n + 6n2 + 9n2 + 2n3)

Combine like terms: 6n2 + 9n2 = 15n2
18 + 31n + 15n2 + 2n3 = (18 + 31n + 15n2 + 2n3)

Add '-18' to each side of the equation.
18 + 31n + 15n2 + -18 + 2n3 = 18 + 31n + 15n2 + -18 + 2n3

Reorder the terms:
18 + -18 + 31n + 15n2 + 2n3 = 18 + 31n + 15n2 + -18 + 2n3

Combine like terms: 18 + -18 = 0
0 + 31n + 15n2 + 2n3 = 18 + 31n + 15n2 + -18 + 2n3
31n + 15n2 + 2n3 = 18 + 31n + 15n2 + -18 + 2n3

Reorder the terms:
31n + 15n2 + 2n3 = 18 + -18 + 31n + 15n2 + 2n3

Combine like terms: 18 + -18 = 0
31n + 15n2 + 2n3 = 0 + 31n + 15n2 + 2n3
31n + 15n2 + 2n3 = 31n + 15n2 + 2n3

Add '-31n' to each side of the equation.
31n + 15n2 + -31n + 2n3 = 31n + 15n2 + -31n + 2n3

Reorder the terms:
31n + -31n + 15n2 + 2n3 = 31n + 15n2 + -31n + 2n3

Combine like terms: 31n + -31n = 0
0 + 15n2 + 2n3 = 31n + 15n2 + -31n + 2n3
15n2 + 2n3 = 31n + 15n2 + -31n + 2n3

Reorder the terms:
15n2 + 2n3 = 31n + -31n + 15n2 + 2n3

Combine like terms: 31n + -31n = 0
15n2 + 2n3 = 0 + 15n2 + 2n3
15n2 + 2n3 = 15n2 + 2n3

Add '-15n2' to each side of the equation.
15n2 + -15n2 + 2n3 = 15n2 + -15n2 + 2n3

Combine like terms: 15n2 + -15n2 = 0
0 + 2n3 = 15n2 + -15n2 + 2n3
2n3 = 15n2 + -15n2 + 2n3

Combine like terms: 15n2 + -15n2 = 0
2n3 = 0 + 2n3
2n3 = 2n3

Add '-2n3' to each side of the equation.
2n3 + -2n3 = 2n3 + -2n3

Combine like terms: 2n3 + -2n3 = 0
0 = 2n3 + -2n3

Combine like terms: 2n3 + -2n3 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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