4x(2x-1)+2(2x-1)=0

Solution for 4x(2x-1)+2(2x-1)=0 equation:

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

Reorder the terms:
4x(-1 + 2x) + 2(2x + -1) = 0
(-1 * 4x + 2x * 4x) + 2(2x + -1) = 0
(-4x + 8x2) + 2(2x + -1) = 0

Reorder the terms:
-4x + 8x2 + 2(-1 + 2x) = 0
-4x + 8x2 + (-1 * 2 + 2x * 2) = 0
-4x + 8x2 + (-2 + 4x) = 0

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

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

Solving
-2 + 8x2 = 0

Solving for variable 'x'.

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

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

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

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

Divide each side by '8'.
x2 = 0.25

Simplifying
x2 = 0.25

Take the square root of each side:
x = {-0.5, 0.5}