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

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

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

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

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

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

Combine like terms: 1n + -20n = -19n
(-4 + -19n + 5n2) = 0

Solving
-4 + -19n + 5n2 = 0

Solving for variable 'n'.

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

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

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

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

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

Divide each side by '-1'.
n = 4

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