4(5n+1)(n+4)=0

Solution for 4(5n+1)(n+4)=0 equation:

Simplifying
4(5n + 1)(n + 4) = 0

Reorder the terms:
4(1 + 5n)(n + 4) = 0

Reorder the terms:
4(1 + 5n)(4 + n) = 0

Multiply (1 + 5n) * (4 + n)
4(1(4 + n) + 5n * (4 + n)) = 0
4((4 * 1 + n * 1) + 5n * (4 + n)) = 0
4((4 + 1n) + 5n * (4 + n)) = 0
4(4 + 1n + (4 * 5n + n * 5n)) = 0
4(4 + 1n + (20n + 5n2)) = 0

Combine like terms: 1n + 20n = 21n
4(4 + 21n + 5n2) = 0
(4 * 4 + 21n * 4 + 5n2 * 4) = 0
(16 + 84n + 20n2) = 0

Solving
16 + 84n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + 21n + 5n2) = 0

Factor a trinomial.
4((4 + n)(1 + 5n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

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

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

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

Simplifying
n = -4
Subproblem 2
Set the factor '(1 + 5n)' equal to zero and attempt to solve:

Simplifying
1 + 5n = 0

Solving
1 + 5n = 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 + 5n = 0 + -1

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

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

Divide each side by '5'.
n = -0.2

Simplifying
n = -0.2
Solution
n = {-4, -0.2}