(4x-8)(8x-4)=0

Solution for (4x-8)(8x-4)=0 equation:

Simplifying
(4x + -8)(8x + -4) = 0

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

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

Multiply (-8 + 4x) * (-4 + 8x)
(-8(-4 + 8x) + 4x * (-4 + 8x)) = 0
((-4 * -8 + 8x * -8) + 4x * (-4 + 8x)) = 0
((32 + -64x) + 4x * (-4 + 8x)) = 0
(32 + -64x + (-4 * 4x + 8x * 4x)) = 0
(32 + -64x + (-16x + 32x2)) = 0

Combine like terms: -64x + -16x = -80x
(32 + -80x + 32x2) = 0

Solving
32 + -80x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(2 + -5x + 2x2) = 0

Factor a trinomial.
16((1 + -2x)(2 + -1x)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.5, 2}