(8x-6)(3x+2)=0

Solution for (8x-6)(3x+2)=0 equation:

Simplifying
(8x + -6)(3x + 2) = 0

Reorder the terms:
(-6 + 8x)(3x + 2) = 0

Reorder the terms:
(-6 + 8x)(2 + 3x) = 0

Multiply (-6 + 8x) * (2 + 3x)
(-6(2 + 3x) + 8x * (2 + 3x)) = 0
((2 * -6 + 3x * -6) + 8x * (2 + 3x)) = 0
((-12 + -18x) + 8x * (2 + 3x)) = 0
(-12 + -18x + (2 * 8x + 3x * 8x)) = 0
(-12 + -18x + (16x + 24x2)) = 0

Combine like terms: -18x + 16x = -2x
(-12 + -2x + 24x2) = 0

Solving
-12 + -2x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1x + 12x2) = 0

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

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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Subproblem 2
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
Solution
x = {-0.6666666667, 0.75}