n(n+1)=600

Solution for n(n+1)=600 equation:

Simplifying
n(n + 1) = 600

Reorder the terms:
n(1 + n) = 600
(1 * n + n * n) = 600
(1n + n2) = 600

Solving
1n + n2 = 600

Solving for variable 'n'.

Reorder the terms:
-600 + 1n + n2 = 600 + -600

Combine like terms: 600 + -600 = 0
-600 + 1n + n2 = 0

Factor a trinomial.
(-25 + -1n)(24 + -1n) = 0

Subproblem 1
Set the factor '(-25 + -1n)' equal to zero and attempt to solve:

Simplifying
-25 + -1n = 0

Solving
-25 + -1n = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1n = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1n = 0 + 25
-1n = 0 + 25

Combine like terms: 0 + 25 = 25
-1n = 25

Divide each side by '-1'.
n = -25

Simplifying
n = -25
Subproblem 2
Set the factor '(24 + -1n)' equal to zero and attempt to solve:

Simplifying
24 + -1n = 0

Solving
24 + -1n = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1n = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1n = 0 + -24
-1n = 0 + -24

Combine like terms: 0 + -24 = -24
-1n = -24

Divide each side by '-1'.
n = 24

Simplifying
n = 24
Solution
n = {-25, 24}