(2n-8)(5n+25)=0

Solution for (2n-8)(5n+25)=0 equation:

Simplifying
(2n + -8)(5n + 25) = 0

Reorder the terms:
(-8 + 2n)(5n + 25) = 0

Reorder the terms:
(-8 + 2n)(25 + 5n) = 0

Multiply (-8 + 2n) * (25 + 5n)
(-8(25 + 5n) + 2n * (25 + 5n)) = 0
((25 * -8 + 5n * -8) + 2n * (25 + 5n)) = 0
((-200 + -40n) + 2n * (25 + 5n)) = 0
(-200 + -40n + (25 * 2n + 5n * 2n)) = 0
(-200 + -40n + (50n + 10n2)) = 0

Combine like terms: -40n + 50n = 10n
(-200 + 10n + 10n2) = 0

Solving
-200 + 10n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-20 + n + n2) = 0

Factor a trinomial.
10((-5 + -1n)(4 + -1n)) = 0

Ignore the factor 10.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

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

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

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-5, 4}