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

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

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

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

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

Multiply (5 + 2n) * (-8 + 2n)
(5(-8 + 2n) + 2n * (-8 + 2n)) = 0
((-8 * 5 + 2n * 5) + 2n * (-8 + 2n)) = 0
((-40 + 10n) + 2n * (-8 + 2n)) = 0
(-40 + 10n + (-8 * 2n + 2n * 2n)) = 0
(-40 + 10n + (-16n + 4n2)) = 0

Combine like terms: 10n + -16n = -6n
(-40 + -6n + 4n2) = 0

Solving
-40 + -6n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -3n + 2n2) = 0

Factor a trinomial.
2((-5 + -2n)(4 + -1n)) = 0

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

Simplifying
-5 + -2n = 0

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

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

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

Divide each side by '-2'.
n = -2.5

Simplifying
n = -2.5
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 = {-2.5, 4}