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

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

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

Reorder the terms:
2x(-2 + x) + 4(x + -2) = 0
(-2 * 2x + x * 2x) + 4(x + -2) = 0
(-4x + 2x2) + 4(x + -2) = 0

Reorder the terms:
-4x + 2x2 + 4(-2 + x) = 0
-4x + 2x2 + (-2 * 4 + x * 4) = 0
-4x + 2x2 + (-8 + 4x) = 0

Reorder the terms:
-8 + -4x + 4x + 2x2 = 0

Combine like terms: -4x + 4x = 0
-8 + 0 + 2x2 = 0
-8 + 2x2 = 0

Solving
-8 + 2x2 = 0

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + 2x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 2x2 = 0 + 8
2x2 = 0 + 8

Combine like terms: 0 + 8 = 8
2x2 = 8

Divide each side by '2'.
x2 = 4

Simplifying
x2 = 4

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