(2n+1)n=1275

Solution for (2n+1)n=1275 equation:

Simplifying
(2n + 1) * n = 1275

Reorder the terms:
(1 + 2n) * n = 1275

Reorder the terms for easier multiplication:
n(1 + 2n) = 1275
(1 * n + 2n * n) = 1275
(1n + 2n2) = 1275

Solving
1n + 2n2 = 1275

Solving for variable 'n'.

Reorder the terms:
-1275 + 1n + 2n2 = 1275 + -1275

Combine like terms: 1275 + -1275 = 0
-1275 + 1n + 2n2 = 0

Factor a trinomial.
(-51 + -2n)(25 + -1n) = 0

Subproblem 1
Set the factor '(-51 + -2n)' equal to zero and attempt to solve:

Simplifying
-51 + -2n = 0

Solving
-51 + -2n = 0

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

Add '51' to each side of the equation.
-51 + 51 + -2n = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -2n = 0 + 51
-2n = 0 + 51

Combine like terms: 0 + 51 = 51
-2n = 51

Divide each side by '-2'.
n = -25.5

Simplifying
n = -25.5
Subproblem 2
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
Solution
n = {-25.5, 25}