(8x-1)(3x-6)=0

Solution for (8x-1)(3x-6)=0 equation:

Simplifying
(8x + -1)(3x + -6) = 0

Reorder the terms:
(-1 + 8x)(3x + -6) = 0

Reorder the terms:
(-1 + 8x)(-6 + 3x) = 0

Multiply (-1 + 8x) * (-6 + 3x)
(-1(-6 + 3x) + 8x * (-6 + 3x)) = 0
((-6 * -1 + 3x * -1) + 8x * (-6 + 3x)) = 0
((6 + -3x) + 8x * (-6 + 3x)) = 0
(6 + -3x + (-6 * 8x + 3x * 8x)) = 0
(6 + -3x + (-48x + 24x2)) = 0

Combine like terms: -3x + -48x = -51x
(6 + -51x + 24x2) = 0

Solving
6 + -51x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -17x + 8x2) = 0

Factor a trinomial.
3((1 + -8x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -8x)' equal to zero and attempt to solve:

Simplifying
1 + -8x = 0

Solving
1 + -8x = 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 + -8x = 0 + -1

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

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

Divide each side by '-8'.
x = 0.125

Simplifying
x = 0.125
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 = {0.125, 2}