(n^2)-(2n)-(3)=0

Solution for (n^2)-(2n)-(3)=0 equation:

Simplifying
(n2) + -1(2n) + -1(3) = 0
n2 + -1(2n) + -1(3) = 0

Remove parenthesis around (2n)
n2 + -1 * 2n + -1(3) = 0

Multiply -1 * 2
n2 + -2n + -1(3) = 0

Multiply -1 * 3
n2 + -2n + -3 = 0

Reorder the terms:
-3 + -2n + n2 = 0

Solving
-3 + -2n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
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 = {-1, 3}