n(2n+3)=275

Solution for n(2n+3)=275 equation:

Simplifying
n(2n + 3) = 275

Reorder the terms:
n(3 + 2n) = 275
(3 * n + 2n * n) = 275
(3n + 2n2) = 275

Solving
3n + 2n2 = 275

Solving for variable 'n'.

Reorder the terms:
-275 + 3n + 2n2 = 275 + -275

Combine like terms: 275 + -275 = 0
-275 + 3n + 2n2 = 0

Factor a trinomial.
(-25 + -2n)(11 + -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 '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Solution
n = {-12.5, 11}