4(5n-10)(2n+5)=0

Solution for 4(5n-10)(2n+5)=0 equation:

Simplifying
4(5n + -10)(2n + 5) = 0

Reorder the terms:
4(-10 + 5n)(2n + 5) = 0

Reorder the terms:
4(-10 + 5n)(5 + 2n) = 0

Multiply (-10 + 5n) * (5 + 2n)
4(-10(5 + 2n) + 5n * (5 + 2n)) = 0
4((5 * -10 + 2n * -10) + 5n * (5 + 2n)) = 0
4((-50 + -20n) + 5n * (5 + 2n)) = 0
4(-50 + -20n + (5 * 5n + 2n * 5n)) = 0
4(-50 + -20n + (25n + 10n2)) = 0

Combine like terms: -20n + 25n = 5n
4(-50 + 5n + 10n2) = 0
(-50 * 4 + 5n * 4 + 10n2 * 4) = 0
(-200 + 20n + 40n2) = 0

Solving
-200 + 20n + 40n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-10 + n + 2n2) = 0

Factor a trinomial.
20((-5 + -2n)(2 + -1n)) = 0

Ignore the factor 20.
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 '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-2.5, 2}