n^2+2n=2400

Solution for n^2+2n=2400 equation:

Simplifying
n2 + 2n = 2400

Reorder the terms:
2n + n2 = 2400

Solving
2n + n2 = 2400

Solving for variable 'n'.

Reorder the terms:
-2400 + 2n + n2 = 2400 + -2400

Combine like terms: 2400 + -2400 = 0
-2400 + 2n + n2 = 0

Factor a trinomial.
(-50 + -1n)(48 + -1n) = 0

Subproblem 1
Set the factor '(-50 + -1n)' equal to zero and attempt to solve:

Simplifying
-50 + -1n = 0

Solving
-50 + -1n = 0

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

Add '50' to each side of the equation.
-50 + 50 + -1n = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1n = 0 + 50
-1n = 0 + 50

Combine like terms: 0 + 50 = 50
-1n = 50

Divide each side by '-1'.
n = -50

Simplifying
n = -50
Subproblem 2
Set the factor '(48 + -1n)' equal to zero and attempt to solve:

Simplifying
48 + -1n = 0

Solving
48 + -1n = 0

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

Add '-48' to each side of the equation.
48 + -48 + -1n = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -1n = 0 + -48
-1n = 0 + -48

Combine like terms: 0 + -48 = -48
-1n = -48

Divide each side by '-1'.
n = 48

Simplifying
n = 48
Solution
n = {-50, 48}