=(2n-4)(n+1)

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

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

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

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

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

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

Solving
0 = -4 + -2n + 2n2

Solving for variable 'n'.

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

Reorder the terms:
4 + 2n + -2n2 = -4 + 4 + -2n + 2n + 2n2 + -2n2

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

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

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

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

Factor a trinomial.
2((2 + -1n)(1 + n)) = 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 '(1 + n)' equal to zero and attempt to solve:

Simplifying
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 = {2, -1}