n(n+2)=35

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

Simplifying
n(n + 2) = 35

Reorder the terms:
n(2 + n) = 35
(2 * n + n * n) = 35
(2n + n2) = 35

Solving
2n + n2 = 35

Solving for variable 'n'.

Reorder the terms:
-35 + 2n + n2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 2n + n2 = 0

Factor a trinomial.
(-7 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-7, 5}