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

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

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

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

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

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

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

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

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

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

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

Multiply (2 + 3n + n2) * (3 + n)
6(2(3 + n) + 3n * (3 + n) + n2(3 + n)) = 80
6((3 * 2 + n * 2) + 3n * (3 + n) + n2(3 + n)) = 80
6((6 + 2n) + 3n * (3 + n) + n2(3 + n)) = 80
6(6 + 2n + (3 * 3n + n * 3n) + n2(3 + n)) = 80
6(6 + 2n + (9n + 3n2) + n2(3 + n)) = 80
6(6 + 2n + 9n + 3n2 + (3 * n2 + n * n2)) = 80
6(6 + 2n + 9n + 3n2 + (3n2 + n3)) = 80

Combine like terms: 2n + 9n = 11n
6(6 + 11n + 3n2 + 3n2 + n3) = 80

Combine like terms: 3n2 + 3n2 = 6n2
6(6 + 11n + 6n2 + n3) = 80
(6 * 6 + 11n * 6 + 6n2 * 6 + n3 * 6) = 80
(36 + 66n + 36n2 + 6n3) = 80

Solving
36 + 66n + 36n2 + 6n3 = 80

Solving for variable 'n'.

Reorder the terms:
36 + -80 + 66n + 36n2 + 6n3 = 80 + -80

Combine like terms: 36 + -80 = -44
-44 + 66n + 36n2 + 6n3 = 80 + -80

Combine like terms: 80 + -80 = 0
-44 + 66n + 36n2 + 6n3 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + 33n + 18n2 + 3n3) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-22 + 33n + 18n2 + 3n3)' equal to zero and attempt to solve:

Simplifying
-22 + 33n + 18n2 + 3n3 = 0

Solving
-22 + 33n + 18n2 + 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.