(2n+1)(n+1)=28

Solution for (2n+1)(n+1)=28 equation:

Simplifying
(2n + 1)(n + 1) = 28

Reorder the terms:
(1 + 2n)(n + 1) = 28

Reorder the terms:
(1 + 2n)(1 + n) = 28

Multiply (1 + 2n) * (1 + n)
(1(1 + n) + 2n * (1 + n)) = 28
((1 * 1 + n * 1) + 2n * (1 + n)) = 28
((1 + 1n) + 2n * (1 + n)) = 28
(1 + 1n + (1 * 2n + n * 2n)) = 28
(1 + 1n + (2n + 2n2)) = 28

Combine like terms: 1n + 2n = 3n
(1 + 3n + 2n2) = 28

Solving
1 + 3n + 2n2 = 28

Solving for variable 'n'.

Reorder the terms:
1 + -28 + 3n + 2n2 = 28 + -28

Combine like terms: 1 + -28 = -27
-27 + 3n + 2n2 = 28 + -28

Combine like terms: 28 + -28 = 0
-27 + 3n + 2n2 = 0

Factor a trinomial.
(-9 + -2n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-9 + -2n)' equal to zero and attempt to solve:

Simplifying
-9 + -2n = 0

Solving
-9 + -2n = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2n = 0 + 9
-2n = 0 + 9

Combine like terms: 0 + 9 = 9
-2n = 9

Divide each side by '-2'.
n = -4.5

Simplifying
n = -4.5
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-4.5, 3}