(n-5)(9n-5)=0

Solution for (n-5)(9n-5)=0 equation:

Simplifying
(n + -5)(9n + -5) = 0

Reorder the terms:
(-5 + n)(9n + -5) = 0

Reorder the terms:
(-5 + n)(-5 + 9n) = 0

Multiply (-5 + n) * (-5 + 9n)
(-5(-5 + 9n) + n(-5 + 9n)) = 0
((-5 * -5 + 9n * -5) + n(-5 + 9n)) = 0
((25 + -45n) + n(-5 + 9n)) = 0
(25 + -45n + (-5 * n + 9n * n)) = 0
(25 + -45n + (-5n + 9n2)) = 0

Combine like terms: -45n + -5n = -50n
(25 + -50n + 9n2) = 0

Solving
25 + -50n + 9n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + -9n)(5 + -1n) = 0

Subproblem 1
Set the factor '(5 + -9n)' equal to zero and attempt to solve:

Simplifying
5 + -9n = 0

Solving
5 + -9n = 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 + -9n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9n = 0 + -5
-9n = 0 + -5

Combine like terms: 0 + -5 = -5
-9n = -5

Divide each side by '-9'.
n = 0.5555555556

Simplifying
n = 0.5555555556
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 = {0.5555555556, 5}