1(n+1)2(n+1)3(n+3)=80

Solution for 1(n+1)2(n+1)3(n+3)=80 equation:

Simplifying
1(n + 1) * 2(n + 1) * 3(n + 3) = 80

Reorder the terms:
1(1 + n) * 2(n + 1) * 3(n + 3) = 80

Reorder the terms:
1(1 + n) * 2(1 + n) * 3(n + 3) = 80

Reorder the terms:
1(1 + n) * 2(1 + n) * 3(3 + n) = 80

Reorder the terms for easier multiplication:
1 * 2 * 3(1 + n)(1 + n)(3 + n) = 80

Multiply 1 * 2
2 * 3(1 + n)(1 + n)(3 + n) = 80

Multiply 2 * 3
6(1 + n)(1 + n)(3 + n) = 80

Multiply (1 + n) * (1 + n)
6(1(1 + n) + n(1 + n))(3 + n) = 80
6((1 * 1 + n * 1) + n(1 + n))(3 + n) = 80
6((1 + 1n) + n(1 + n))(3 + n) = 80
6(1 + 1n + (1 * n + n * n))(3 + n) = 80
6(1 + 1n + (1n + n2))(3 + n) = 80

Combine like terms: 1n + 1n = 2n
6(1 + 2n + n2)(3 + n) = 80

Multiply (1 + 2n + n2) * (3 + n)
6(1(3 + n) + 2n * (3 + n) + n2(3 + n)) = 80
6((3 * 1 + n * 1) + 2n * (3 + n) + n2(3 + n)) = 80
6((3 + 1n) + 2n * (3 + n) + n2(3 + n)) = 80
6(3 + 1n + (3 * 2n + n * 2n) + n2(3 + n)) = 80
6(3 + 1n + (6n + 2n2) + n2(3 + n)) = 80
6(3 + 1n + 6n + 2n2 + (3 * n2 + n * n2)) = 80
6(3 + 1n + 6n + 2n2 + (3n2 + n3)) = 80

Combine like terms: 1n + 6n = 7n
6(3 + 7n + 2n2 + 3n2 + n3) = 80

Combine like terms: 2n2 + 3n2 = 5n2
6(3 + 7n + 5n2 + n3) = 80
(3 * 6 + 7n * 6 + 5n2 * 6 + n3 * 6) = 80
(18 + 42n + 30n2 + 6n3) = 80

Solving
18 + 42n + 30n2 + 6n3 = 80

Solving for variable 'n'.

Reorder the terms:
18 + -80 + 42n + 30n2 + 6n3 = 80 + -80

Combine like terms: 18 + -80 = -62
-62 + 42n + 30n2 + 6n3 = 80 + -80

Combine like terms: 80 + -80 = 0
-62 + 42n + 30n2 + 6n3 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + 21n + 15n2 + 3n3) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-31 + 21n + 15n2 + 3n3)' equal to zero and attempt to solve:

Simplifying
-31 + 21n + 15n2 + 3n3 = 0

Solving
-31 + 21n + 15n2 + 3n3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.