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

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

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

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

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

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

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

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

Solving for variable 'n'.

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

Reorder the terms:
20 + 6n + -2n2 = -20 + 20 + -6n + 6n + 2n2 + -2n2

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 3n + -1n2) = 0

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

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

Simplifying
2 + n = 0

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

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

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

Simplifying
n = -2
Solution
n = {5, -2}