(2x-12)(8x-4)=0

Solution for (2x-12)(8x-4)=0 equation:

Simplifying
(2x + -12)(8x + -4) = 0

Reorder the terms:
(-12 + 2x)(8x + -4) = 0

Reorder the terms:
(-12 + 2x)(-4 + 8x) = 0

Multiply (-12 + 2x) * (-4 + 8x)
(-12(-4 + 8x) + 2x * (-4 + 8x)) = 0
((-4 * -12 + 8x * -12) + 2x * (-4 + 8x)) = 0
((48 + -96x) + 2x * (-4 + 8x)) = 0
(48 + -96x + (-4 * 2x + 8x * 2x)) = 0
(48 + -96x + (-8x + 16x2)) = 0

Combine like terms: -96x + -8x = -104x
(48 + -104x + 16x2) = 0

Solving
48 + -104x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(6 + -13x + 2x2) = 0

Factor a trinomial.
8((1 + -2x)(6 + -1x)) = 0

Ignore the factor 8.
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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0.5, 6}