(8x+6)(2x-1)=0

Solution for (8x+6)(2x-1)=0 equation:

Simplifying
(8x + 6)(2x + -1) = 0

Reorder the terms:
(6 + 8x)(2x + -1) = 0

Reorder the terms:
(6 + 8x)(-1 + 2x) = 0

Multiply (6 + 8x) * (-1 + 2x)
(6(-1 + 2x) + 8x * (-1 + 2x)) = 0
((-1 * 6 + 2x * 6) + 8x * (-1 + 2x)) = 0
((-6 + 12x) + 8x * (-1 + 2x)) = 0
(-6 + 12x + (-1 * 8x + 2x * 8x)) = 0
(-6 + 12x + (-8x + 16x2)) = 0

Combine like terms: 12x + -8x = 4x
(-6 + 4x + 16x2) = 0

Solving
-6 + 4x + 16x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
2((-3 + -4x)(1 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-0.75, 0.5}