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

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

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

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

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

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

Combine like terms: 1n + -5n = -4n
2(-1 + -4n + 5n2) = 0
(-1 * 2 + -4n * 2 + 5n2 * 2) = 0
(-2 + -8n + 10n2) = 0

Solving
-2 + -8n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -4n + 5n2) = 0

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

Ignore the factor 2.
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 '(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 = {-0.2, 1}