(n-1)(5n-2)=0

Solution for (n-1)(5n-2)=0 equation:

Simplifying
(n + -1)(5n + -2) = 0

Reorder the terms:
(-1 + n)(5n + -2) = 0

Reorder the terms:
(-1 + n)(-2 + 5n) = 0

Multiply (-1 + n) * (-2 + 5n)
(-1(-2 + 5n) + n(-2 + 5n)) = 0
((-2 * -1 + 5n * -1) + n(-2 + 5n)) = 0
((2 + -5n) + n(-2 + 5n)) = 0
(2 + -5n + (-2 * n + 5n * n)) = 0
(2 + -5n + (-2n + 5n2)) = 0

Combine like terms: -5n + -2n = -7n
(2 + -7n + 5n2) = 0

Solving
2 + -7n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + -5n)(1 + -1n) = 0

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

Simplifying
2 + -5n = 0

Solving
2 + -5n = 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 + -5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5n = 0 + -2
-5n = 0 + -2

Combine like terms: 0 + -2 = -2
-5n = -2

Divide each side by '-5'.
n = 0.4

Simplifying
n = 0.4
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

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

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

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

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

Simplifying
n = 1
Solution
n = {0.4, 1}