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

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

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

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

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

Multiply (1 + 3n) * (-3 + n)
(1(-3 + n) + 3n * (-3 + n)) = 0
((-3 * 1 + n * 1) + 3n * (-3 + n)) = 0
((-3 + 1n) + 3n * (-3 + n)) = 0
(-3 + 1n + (-3 * 3n + n * 3n)) = 0
(-3 + 1n + (-9n + 3n2)) = 0

Combine like terms: 1n + -9n = -8n
(-3 + -8n + 3n2) = 0

Solving
-3 + -8n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -3n)(3 + -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 '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-0.3333333333, 3}