(1n+2)(2n+5)=0

Solution for (1n+2)(2n+5)=0 equation:

Simplifying
(1n + 2)(2n + 5) = 0

Reorder the terms:
(2 + 1n)(2n + 5) = 0

Reorder the terms:
(2 + 1n)(5 + 2n) = 0

Multiply (2 + 1n) * (5 + 2n)
(2(5 + 2n) + 1n * (5 + 2n)) = 0
((5 * 2 + 2n * 2) + 1n * (5 + 2n)) = 0
((10 + 4n) + 1n * (5 + 2n)) = 0
(10 + 4n + (5 * 1n + 2n * 1n)) = 0
(10 + 4n + (5n + 2n2)) = 0

Combine like terms: 4n + 5n = 9n
(10 + 9n + 2n2) = 0

Solving
10 + 9n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + 2n)(2 + n) = 0

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

Simplifying
5 + 2n = 0

Solving
5 + 2n = 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 + 2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2n = 0 + -5
2n = 0 + -5

Combine like terms: 0 + -5 = -5
2n = -5

Divide each side by '2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {-2.5, -2}