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

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

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

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

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

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

Combine like terms: 2n + 10n = 12n
(4 + 12n + 5n2) = 0

Solving
4 + 12n + 5n2 = 0

Solving for variable 'n'.

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

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

Simplifying
2 + 5n = 0

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

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

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

Divide each side by '5'.
n = -0.4

Simplifying
n = -0.4
Solution
n = {-2, -0.4}