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

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

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

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

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

Multiply (-8 + x) * (-2 + 8x)
(-8(-2 + 8x) + x(-2 + 8x)) = 0
((-2 * -8 + 8x * -8) + x(-2 + 8x)) = 0
((16 + -64x) + x(-2 + 8x)) = 0
(16 + -64x + (-2 * x + 8x * x)) = 0
(16 + -64x + (-2x + 8x2)) = 0

Combine like terms: -64x + -2x = -66x
(16 + -66x + 8x2) = 0

Solving
16 + -66x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -33x + 4x2) = 0

Factor a trinomial.
2((1 + -4x)(8 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0.25, 8}