10000n+10000=n^2-1

Solution for 10000n+10000=n^2-1 equation:

Simplifying
10000n + 10000 = n2 + -1

Reorder the terms:
10000 + 10000n = n2 + -1

Reorder the terms:
10000 + 10000n = -1 + n2

Solving
10000 + 10000n = -1 + n2

Solving for variable 'n'.

Reorder the terms:
10000 + 1 + 10000n + -1n2 = -1 + n2 + 1 + -1n2

Combine like terms: 10000 + 1 = 10001
10001 + 10000n + -1n2 = -1 + n2 + 1 + -1n2

Reorder the terms:
10001 + 10000n + -1n2 = -1 + 1 + n2 + -1n2

Combine like terms: -1 + 1 = 0
10001 + 10000n + -1n2 = 0 + n2 + -1n2
10001 + 10000n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
10001 + 10000n + -1n2 = 0

Factor a trinomial.
(10001 + -1n)(1 + n) = 0

Subproblem 1
Set the factor '(10001 + -1n)' equal to zero and attempt to solve:

Simplifying
10001 + -1n = 0

Solving
10001 + -1n = 0

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

Add '-10001' to each side of the equation.
10001 + -10001 + -1n = 0 + -10001

Combine like terms: 10001 + -10001 = 0
0 + -1n = 0 + -10001
-1n = 0 + -10001

Combine like terms: 0 + -10001 = -10001
-1n = -10001

Divide each side by '-1'.
n = 10001

Simplifying
n = 10001
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 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 + n = 0 + -1

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

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

Simplifying
n = -1
Solution
n = {10001, -1}