(4x-2)(8x+3)=0

Solution for (4x-2)(8x+3)=0 equation:

Simplifying
(4x + -2)(8x + 3) = 0

Reorder the terms:
(-2 + 4x)(8x + 3) = 0

Reorder the terms:
(-2 + 4x)(3 + 8x) = 0

Multiply (-2 + 4x) * (3 + 8x)
(-2(3 + 8x) + 4x * (3 + 8x)) = 0
((3 * -2 + 8x * -2) + 4x * (3 + 8x)) = 0
((-6 + -16x) + 4x * (3 + 8x)) = 0
(-6 + -16x + (3 * 4x + 8x * 4x)) = 0
(-6 + -16x + (12x + 32x2)) = 0

Combine like terms: -16x + 12x = -4x
(-6 + -4x + 32x2) = 0

Solving
-6 + -4x + 32x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -8x)' equal to zero and attempt to solve:

Simplifying
-3 + -8x = 0

Solving
-3 + -8x = 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 + -8x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8x = 0 + 3
-8x = 0 + 3

Combine like terms: 0 + 3 = 3
-8x = 3

Divide each side by '-8'.
x = -0.375

Simplifying
x = -0.375
Subproblem 2
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
Solution
x = {-0.375, 0.5}