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

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

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

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

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

Multiply (-1 + 5n) * (-5 + n)
(-1(-5 + n) + 5n * (-5 + n)) = 0
((-5 * -1 + n * -1) + 5n * (-5 + n)) = 0
((5 + -1n) + 5n * (-5 + n)) = 0
(5 + -1n + (-5 * 5n + n * 5n)) = 0
(5 + -1n + (-25n + 5n2)) = 0

Combine like terms: -1n + -25n = -26n
(5 + -26n + 5n2) = 0

Solving
5 + -26n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -5n)(5 + -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 '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

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

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

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

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {0.2, 5}