0=(4x-1)(-8x+6)

Solution for 0=(4x-1)(-8x+6) equation:

Simplifying
0 = (4x + -1)(-8x + 6)

Reorder the terms:
0 = (-1 + 4x)(-8x + 6)

Reorder the terms:
0 = (-1 + 4x)(6 + -8x)

Multiply (-1 + 4x) * (6 + -8x)
0 = (-1(6 + -8x) + 4x * (6 + -8x))
0 = ((6 * -1 + -8x * -1) + 4x * (6 + -8x))
0 = ((-6 + 8x) + 4x * (6 + -8x))
0 = (-6 + 8x + (6 * 4x + -8x * 4x))
0 = (-6 + 8x + (24x + -32x2))

Combine like terms: 8x + 24x = 32x
0 = (-6 + 32x + -32x2)

Solving
0 = -6 + 32x + -32x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -32x + 32x2 = -6 + 32x + -32x2 + 6 + -32x + 32x2

Reorder the terms:
6 + -32x + 32x2 = -6 + 6 + 32x + -32x + -32x2 + 32x2

Combine like terms: -6 + 6 = 0
6 + -32x + 32x2 = 0 + 32x + -32x + -32x2 + 32x2
6 + -32x + 32x2 = 32x + -32x + -32x2 + 32x2

Combine like terms: 32x + -32x = 0
6 + -32x + 32x2 = 0 + -32x2 + 32x2
6 + -32x + 32x2 = -32x2 + 32x2

Combine like terms: -32x2 + 32x2 = 0
6 + -32x + 32x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -16x + 16x2) = 0

Factor a trinomial.
2((1 + -4x)(3 + -4x)) = 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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0.25, 0.75}