(2nx-4)(nx+2)=0

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

Simplifying
(2nx + -4)(nx + 2) = 0

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

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

Multiply (-4 + 2nx) * (2 + nx)
(-4(2 + nx) + 2nx * (2 + nx)) = 0
((2 * -4 + nx * -4) + 2nx * (2 + nx)) = 0
((-8 + -4nx) + 2nx * (2 + nx)) = 0
(-8 + -4nx + (2 * 2nx + nx * 2nx)) = 0
(-8 + -4nx + (4nx + 2n2x2)) = 0

Combine like terms: -4nx + 4nx = 0
(-8 + 0 + 2n2x2) = 0
(-8 + 2n2x2) = 0

Solving
-8 + 2n2x2 = 0

Solving for variable 'n'.

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

Add '8' to each side of the equation.
-8 + 8 + 2n2x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 2n2x2 = 0 + 8
2n2x2 = 0 + 8

Combine like terms: 0 + 8 = 8
2n2x2 = 8

Divide each side by '2x2'.
n2 = 4x-2

Simplifying
n2 = 4x-2

Take the square root of each side:
n = {-2x-1, 2x-1}