(n+2)(4n+1)=0

Solution for (n+2)(4n+1)=0 equation:

Simplifying
(n + 2)(4n + 1) = 0

Reorder the terms:
(2 + n)(4n + 1) = 0

Reorder the terms:
(2 + n)(1 + 4n) = 0

Multiply (2 + n) * (1 + 4n)
(2(1 + 4n) + n(1 + 4n)) = 0
((1 * 2 + 4n * 2) + n(1 + 4n)) = 0
((2 + 8n) + n(1 + 4n)) = 0
(2 + 8n + (1 * n + 4n * n)) = 0
(2 + 8n + (1n + 4n2)) = 0

Combine like terms: 8n + 1n = 9n
(2 + 9n + 4n2) = 0

Solving
2 + 9n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + n)(1 + 4n) = 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 '(1 + 4n)' equal to zero and attempt to solve:

Simplifying
1 + 4n = 0

Solving
1 + 4n = 0

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

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

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

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

Divide each side by '4'.
n = -0.25

Simplifying
n = -0.25
Solution
n = {-2, -0.25}