4y(2n-10)(n+1)=0

Solution for 4y(2n-10)(n+1)=0 equation:

Simplifying
4y(2n + -10)(n + 1) = 0

Reorder the terms:
4y(-10 + 2n)(n + 1) = 0

Reorder the terms:
4y(-10 + 2n)(1 + n) = 0

Multiply (-10 + 2n) * (1 + n)
4y(-10(1 + n) + 2n * (1 + n)) = 0
4y((1 * -10 + n * -10) + 2n * (1 + n)) = 0
4y((-10 + -10n) + 2n * (1 + n)) = 0
4y(-10 + -10n + (1 * 2n + n * 2n)) = 0
4y(-10 + -10n + (2n + 2n2)) = 0

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

Reorder the terms:
(-32ny + 8n2y + -40y) = 0
(-32ny + 8n2y + -40y) = 0

Solving
-32ny + 8n2y + -40y = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8y'.
8y(-4n + n2 + -5) = 0

Factor a trinomial.
8y((n + -5)(n + 1)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(n + -5)' equal to zero and attempt to solve:

Simplifying
n + -5 = 0

Reorder the terms:
-5 + n = 0

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

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

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

Simplifying
n = 5
Subproblem 3
Set the factor '(n + 1)' equal to zero and attempt to solve:

Simplifying
n + 1 = 0

Reorder the terms:
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
Solution
n = {5, -1}