(2n-8)(n+4)=0

Solution for (2n-8)(n+4)=0 equation:

Simplifying
(2n + -8)(n + 4) = 0

Reorder the terms:
(-8 + 2n)(n + 4) = 0

Reorder the terms:
(-8 + 2n)(4 + n) = 0

Multiply (-8 + 2n) * (4 + n)
(-8(4 + n) + 2n * (4 + n)) = 0
((4 * -8 + n * -8) + 2n * (4 + n)) = 0
((-32 + -8n) + 2n * (4 + n)) = 0
(-32 + -8n + (4 * 2n + n * 2n)) = 0
(-32 + -8n + (8n + 2n2)) = 0

Combine like terms: -8n + 8n = 0
(-32 + 0 + 2n2) = 0
(-32 + 2n2) = 0

Solving
-32 + 2n2 = 0

Solving for variable 'n'.

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

Add '32' to each side of the equation.
-32 + 32 + 2n2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 2n2 = 0 + 32
2n2 = 0 + 32

Combine like terms: 0 + 32 = 32
2n2 = 32

Divide each side by '2'.
n2 = 16

Simplifying
n2 = 16

Take the square root of each side:
n = {-4, 4}