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

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

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

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

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

Multiply (-1 + 6x) * (4 + 8x)
(-1(4 + 8x) + 6x * (4 + 8x)) = 0
((4 * -1 + 8x * -1) + 6x * (4 + 8x)) = 0
((-4 + -8x) + 6x * (4 + 8x)) = 0
(-4 + -8x + (4 * 6x + 8x * 6x)) = 0
(-4 + -8x + (24x + 48x2)) = 0

Combine like terms: -8x + 24x = 16x
(-4 + 16x + 48x2) = 0

Solving
-4 + 16x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 4x + 12x2) = 0

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

Ignore the factor 4.
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 '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

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

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

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {-0.5, 0.1666666667}