n(2n+1)=300

Solution for n(2n+1)=300 equation:

Simplifying
n(2n + 1) = 300

Reorder the terms:
n(1 + 2n) = 300
(1 * n + 2n * n) = 300
(1n + 2n2) = 300

Solving
1n + 2n2 = 300

Solving for variable 'n'.

Reorder the terms:
-300 + 1n + 2n2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + 1n + 2n2 = 0

Factor a trinomial.
(-25 + -2n)(12 + -1n) = 0

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

Simplifying
-25 + -2n = 0

Solving
-25 + -2n = 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 + -2n = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2n = 0 + 25
-2n = 0 + 25

Combine like terms: 0 + 25 = 25
-2n = 25

Divide each side by '-2'.
n = -12.5

Simplifying
n = -12.5
Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {-12.5, 12}