21n(x+3)+1n(x-1)=0

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Solution for 21n(x+3)+1n(x-1)=0 equation: 


Simplifying
21n(x + 3) + 1n(x + -1) = 0

Reorder the terms:
21n(3 + x) + 1n(x + -1) = 0
(3 * 21n + x * 21n) + 1n(x + -1) = 0
(63n + 21nx) + 1n(x + -1) = 0

Reorder the terms:
63n + 21nx + 1n(-1 + x) = 0
63n + 21nx + (-1 * 1n + x * 1n) = 0
63n + 21nx + (-1n + 1nx) = 0

Reorder the terms:
63n + -1n + 21nx + 1nx = 0

Combine like terms: 63n + -1n = 62n
62n + 21nx + 1nx = 0

Combine like terms: 21nx + 1nx = 22nx
62n + 22nx = 0

Solving
62n + 22nx = 0

Solving for variable 'n'.

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

Factor out the Greatest Common Factor (GCF), '2n'.
2n(31 + 11x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(31 + 11x)' equal to zero and attempt to solve:

Simplifying
31 + 11x = 0

Solving
31 + 11x = 0

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

Add '-31' to each side of the equation.
31 + -31 + 11x = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 11x = 0 + -31
11x = 0 + -31

Combine like terms: 0 + -31 = -31
11x = -31

Add '-11x' to each side of the equation.
11x + -11x = -31 + -11x

Combine like terms: 11x + -11x = 0
0 = -31 + -11x

Simplifying
0 = -31 + -11x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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