(4x-6)(8x+2)=0

Solution for (4x-6)(8x+2)=0 equation:

Simplifying
(4x + -6)(8x + 2) = 0

Reorder the terms:
(-6 + 4x)(8x + 2) = 0

Reorder the terms:
(-6 + 4x)(2 + 8x) = 0

Multiply (-6 + 4x) * (2 + 8x)
(-6(2 + 8x) + 4x * (2 + 8x)) = 0
((2 * -6 + 8x * -6) + 4x * (2 + 8x)) = 0
((-12 + -48x) + 4x * (2 + 8x)) = 0
(-12 + -48x + (2 * 4x + 8x * 4x)) = 0
(-12 + -48x + (8x + 32x2)) = 0

Combine like terms: -48x + 8x = -40x
(-12 + -40x + 32x2) = 0

Solving
-12 + -40x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -10x + 8x2) = 0

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

Ignore the factor 4.
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 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.25, 1.5}