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

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

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

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

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

Multiply (-2 + 5n) * (-2 + 2n)
n(-2(-2 + 2n) + 5n * (-2 + 2n)) = 0
n((-2 * -2 + 2n * -2) + 5n * (-2 + 2n)) = 0
n((4 + -4n) + 5n * (-2 + 2n)) = 0
n(4 + -4n + (-2 * 5n + 2n * 5n)) = 0
n(4 + -4n + (-10n + 10n2)) = 0

Combine like terms: -4n + -10n = -14n
n(4 + -14n + 10n2) = 0
(4 * n + -14n * n + 10n2 * n) = 0
(4n + -14n2 + 10n3) = 0

Solving
4n + -14n2 + 10n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(2 + -7n + 5n2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
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 3
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, 0.4, 1}