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

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

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

Reorder the terms:
2n(-5 + n) + 4(n + -5) = 0
(-5 * 2n + n * 2n) + 4(n + -5) = 0
(-10n + 2n2) + 4(n + -5) = 0

Reorder the terms:
-10n + 2n2 + 4(-5 + n) = 0
-10n + 2n2 + (-5 * 4 + n * 4) = 0
-10n + 2n2 + (-20 + 4n) = 0

Reorder the terms:
-20 + -10n + 4n + 2n2 = 0

Combine like terms: -10n + 4n = -6n
-20 + -6n + 2n2 = 0

Solving
-20 + -6n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -3n + n2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
n = {-2, 5}