(x-6)(4x-8)=0

Solution for (x-6)(4x-8)=0 equation:

Simplifying
(x + -6)(4x + -8) = 0

Reorder the terms:
(-6 + x)(4x + -8) = 0

Reorder the terms:
(-6 + x)(-8 + 4x) = 0

Multiply (-6 + x) * (-8 + 4x)
(-6(-8 + 4x) + x(-8 + 4x)) = 0
((-8 * -6 + 4x * -6) + x(-8 + 4x)) = 0
((48 + -24x) + x(-8 + 4x)) = 0
(48 + -24x + (-8 * x + 4x * x)) = 0
(48 + -24x + (-8x + 4x2)) = 0

Combine like terms: -24x + -8x = -32x
(48 + -32x + 4x2) = 0

Solving
48 + -32x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + -8x + x2) = 0

Factor a trinomial.
4((2 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
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
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 = {2, 6}