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

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

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

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

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

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

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