n(n+2)=675

Solution for n(n+2)=675 equation:

Simplifying
n(n + 2) = 675

Reorder the terms:
n(2 + n) = 675
(2 * n + n * n) = 675
(2n + n2) = 675

Solving
2n + n2 = 675

Solving for variable 'n'.

Reorder the terms:
-675 + 2n + n2 = 675 + -675

Combine like terms: 675 + -675 = 0
-675 + 2n + n2 = 0

Factor a trinomial.
(-27 + -1n)(25 + -1n) = 0

Subproblem 1
Set the factor '(-27 + -1n)' equal to zero and attempt to solve:

Simplifying
-27 + -1n = 0

Solving
-27 + -1n = 0

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

Add '27' to each side of the equation.
-27 + 27 + -1n = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1n = 0 + 27
-1n = 0 + 27

Combine like terms: 0 + 27 = 27
-1n = 27

Divide each side by '-1'.
n = -27

Simplifying
n = -27
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 = {-27, 25}