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

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

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

Reorder the terms:
(-1 + n)(3n + 1) = 0

Reorder the terms:
(-1 + n)(1 + 3n) = 0

Multiply (-1 + n) * (1 + 3n)
(-1(1 + 3n) + n(1 + 3n)) = 0
((1 * -1 + 3n * -1) + n(1 + 3n)) = 0
((-1 + -3n) + n(1 + 3n)) = 0
(-1 + -3n + (1 * n + 3n * n)) = 0
(-1 + -3n + (1n + 3n2)) = 0

Combine like terms: -3n + 1n = -2n
(-1 + -2n + 3n2) = 0

Solving
-1 + -2n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -3n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-1 + -3n)' equal to zero and attempt to solve:

Simplifying
-1 + -3n = 0

Solving
-1 + -3n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3n = 0 + 1
-3n = 0 + 1

Combine like terms: 0 + 1 = 1
-3n = 1

Divide each side by '-3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {-0.3333333333, 1}