(-8n-2)(5n+5)=0

Solution for (-8n-2)(5n+5)=0 equation:

Simplifying
(-8n + -2)(5n + 5) = 0

Reorder the terms:
(-2 + -8n)(5n + 5) = 0

Reorder the terms:
(-2 + -8n)(5 + 5n) = 0

Multiply (-2 + -8n) * (5 + 5n)
(-2(5 + 5n) + -8n * (5 + 5n)) = 0
((5 * -2 + 5n * -2) + -8n * (5 + 5n)) = 0
((-10 + -10n) + -8n * (5 + 5n)) = 0
(-10 + -10n + (5 * -8n + 5n * -8n)) = 0
(-10 + -10n + (-40n + -40n2)) = 0

Combine like terms: -10n + -40n = -50n
(-10 + -50n + -40n2) = 0

Solving
-10 + -50n + -40n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-10'.
-10(1 + 5n + 4n2) = 0

Factor a trinomial.
-10((1 + n)(1 + 4n)) = 0

Ignore the factor -10.
Subproblem 1
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

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

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

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

Simplifying
n = -1
Subproblem 2
Set the factor '(1 + 4n)' equal to zero and attempt to solve:

Simplifying
1 + 4n = 0

Solving
1 + 4n = 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 + 4n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4n = 0 + -1
4n = 0 + -1

Combine like terms: 0 + -1 = -1
4n = -1

Divide each side by '4'.
n = -0.25

Simplifying
n = -0.25
Solution
n = {-1, -0.25}