n(n+1)=4002000

Solution for n(n+1)=4002000 equation:

Simplifying
n(n + 1) = 4002000

Reorder the terms:
n(1 + n) = 4002000
(1 * n + n * n) = 4002000
(1n + n2) = 4002000

Solving
1n + n2 = 4002000

Solving for variable 'n'.

Reorder the terms:
-4002000 + 1n + n2 = 4002000 + -4002000

Combine like terms: 4002000 + -4002000 = 0
-4002000 + 1n + n2 = 0

Factor a trinomial.
(-2001 + -1n)(2000 + -1n) = 0

Subproblem 1
Set the factor '(-2001 + -1n)' equal to zero and attempt to solve:

Simplifying
-2001 + -1n = 0

Solving
-2001 + -1n = 0

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

Add '2001' to each side of the equation.
-2001 + 2001 + -1n = 0 + 2001

Combine like terms: -2001 + 2001 = 0
0 + -1n = 0 + 2001
-1n = 0 + 2001

Combine like terms: 0 + 2001 = 2001
-1n = 2001

Divide each side by '-1'.
n = -2001

Simplifying
n = -2001
Subproblem 2
Set the factor '(2000 + -1n)' equal to zero and attempt to solve:

Simplifying
2000 + -1n = 0

Solving
2000 + -1n = 0

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

Add '-2000' to each side of the equation.
2000 + -2000 + -1n = 0 + -2000

Combine like terms: 2000 + -2000 = 0
0 + -1n = 0 + -2000
-1n = 0 + -2000

Combine like terms: 0 + -2000 = -2000
-1n = -2000

Divide each side by '-1'.
n = 2000

Simplifying
n = 2000
Solution
n = {-2001, 2000}