(2n+1)(2n+3)=35

Solution for (2n+1)(2n+3)=35 equation:

Simplifying
(2n + 1)(2n + 3) = 35

Reorder the terms:
(1 + 2n)(2n + 3) = 35

Reorder the terms:
(1 + 2n)(3 + 2n) = 35

Multiply (1 + 2n) * (3 + 2n)
(1(3 + 2n) + 2n * (3 + 2n)) = 35
((3 * 1 + 2n * 1) + 2n * (3 + 2n)) = 35
((3 + 2n) + 2n * (3 + 2n)) = 35
(3 + 2n + (3 * 2n + 2n * 2n)) = 35
(3 + 2n + (6n + 4n2)) = 35

Combine like terms: 2n + 6n = 8n
(3 + 8n + 4n2) = 35

Solving
3 + 8n + 4n2 = 35

Solving for variable 'n'.

Reorder the terms:
3 + -35 + 8n + 4n2 = 35 + -35

Combine like terms: 3 + -35 = -32
-32 + 8n + 4n2 = 35 + -35

Combine like terms: 35 + -35 = 0
-32 + 8n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 2n + n2) = 0

Factor a trinomial.
4((-4 + -1n)(2 + -1n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

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

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

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-4, 2}