(3x-1)(8x+4)=0

Solution for (3x-1)(8x+4)=0 equation:

Simplifying
(3x + -1)(8x + 4) = 0

Reorder the terms:
(-1 + 3x)(8x + 4) = 0

Reorder the terms:
(-1 + 3x)(4 + 8x) = 0

Multiply (-1 + 3x) * (4 + 8x)
(-1(4 + 8x) + 3x * (4 + 8x)) = 0
((4 * -1 + 8x * -1) + 3x * (4 + 8x)) = 0
((-4 + -8x) + 3x * (4 + 8x)) = 0
(-4 + -8x + (4 * 3x + 8x * 3x)) = 0
(-4 + -8x + (12x + 24x2)) = 0

Combine like terms: -8x + 12x = 4x
(-4 + 4x + 24x2) = 0

Solving
-4 + 4x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + x + 6x2) = 0

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-0.5, 0.3333333333}